Short Answer: No
But proficiency with an Herbalism Kit represents training, knowledge, and skill in medicinal plants and herbs, for the purpose of healing injury and treating wounds. The training and know-how to weaponize or hide substances to create poison is part of what makes one proficient with a Poisoner's Kit
You might be able to try, with DM permission, as there is some overlap between a Poisoner's Kit and an Herbalism Kit (and possibly even Alchemist's Supplies), whereas one untrained in all three wouldn't be able to make an attempt at all. But unless you have proficiency as both a Poisoner and Herbalist, the most likely result is a dead Herbalist, a fouled or destroyed Kit, and an intended “victim” with little more than indigestion.
Detailed Answer: Still "no".
Tool Proficiency is training and knowledge in specific, limited skills and activities. Different "Proficiency" represents different skills and activities. Overlap might exist, but since the tool descriptions don't mention it, it's not RAW or RAI. Your DM might allow it with disadvantages or difficulty. Poisons, herbs, plants, chemicals, are all mentioned as separate substances requiring different training and knowledge to safely and effectively collect, handle, refine, etc. An Herbalism Kit is specific in that it deals with only the medicinal properties of only plants and herbs.
An Herbalism Kit lets a character identify a poison, but it's not an easy or trivial attempt (DC 20). If it's a challenge to merely identify a poison, it would be even harder, and likely impossible, to effectively and safely create one. That training and knowledge in how to use plants to poison or harm creatures is part of what makes up, well, a Poisoner's Kit proficiency.
Rulebook definitions (truncated, emphasis mine):
TOOLS (Player's Handbook, pg 154)
A tool helps you to do something you couldn't otherwise do ... Proficiency with a tool allows you to add your proficiency bonus to any ability check you make using that tool. … [P]roficiency with a tool represents broader knowledge of its use. For example, the DM might ask you to make a Dexterity check to carve a fine detail with your woodcarver's tools, or a Strength check to make something out of particularly hard wood.
Let's focus on Carpenter's Tools, since that is the example in the books. Different Ability scores might apply, but the checks still pertain to that tool and what that tool is designed to do. This is why a “Strength check to make something” still clarifies “out of wood”, and not stone or metal. The DMG elaborates why doesn’t this apply to everything:
TOOLS (Dungeon Master's Guide pg 239)
Having proficiency with a tool allows you to apply your proficiency bonus to an ability check you make using that tool. For example, a character proficient with carpenter's tools can apply their proficiency bonus to a Dexterity check to craft a wooden flute, an Intelligence check to craft a wooden secret door, or a Strength check to build a working trebuchet [trebuchets are built from wood]. However, the proficiency bonus wouldn't apply to an ability check made to identify unsafe wooden construction or to discern the origin of a crafted item, since neither check requires tool use.
Proficiency with Carpenter's Tools does not* represent a wider knowledge of History (origins of an item) or Investigation/Perception (is this bridge sturdy?). It only represents limited, specialized knowledge and training for specific purposes involving use of appropriate tools: creating or repairing objects made of wood. In the same way, Herbalism Kit proficiency includes training in poison identification for the purpose of using medicinal plants for healing, but not for creating or administering poison to cause harm.
A kit's components are specialized as well. Carpenter's Tools and Smith's Tools each include a "hammer", but a hammer suited to forge-weld metal is ill-suited for tapping a woodworking chisel. An Herbalism and Poisoner's Kits might share similar components, but they are not identical: they are distinctly specialized for differing purposes. Poisons or chemicals could taint, foul, or damage the Herbalism Kit, because it’s not designed (and you're not trained) to work with them.
Herbalism Kit proficiency also mentions "safely collect" useful elements of plants, but since the focus is on health, this "safety" likely means "without contamination": Keep bad stuff out of a patient. The "safely" involved in poisons, however, means "not killing yourself": collect bad stuff and keep it off of you.
Xanathar's Guide to Everything gives more specific detail about what different tools can do and what a proficient character can do with them. I’ll include Alchemist's Supplies too, since they also seem similar to an Herbalism or Poisoner's Kit:
ALCHEMIST'S SUPPLIES (XGE pg 79)
...enable a character to produce useful concoctions, such as acid or alchemist’s fire.
- Components. glass beakers, metal frame (hold beaker over flame), glass stirring rod, mortar & pestle, pouch of alchemical ingredients (salt, powdered iron, purified water)
- Arcana. more info on checks involving potions and similar materials
- Investigation. Insight into chemicals or other substances used in an area
- Alchemical Crafting. create alchemical items: dose of acid, alchemist’s fire, antitoxin, oil, perfume, soap
- Activities. Create a puff of thick smoke (DC10); Identify a poison (DC10); Identify a substance (DC15); Start a fire (DC15); Neutralize acid (DC20)
HERBALISM KIT (XGE pg 82)
... allows you to identify plants and safely collect their useful elements.
- Components: pouches, clippers & gloves for collect plants, mortar & pestle, glass jars
- Arcana: add insight to magical studies deal with plants or identify potions
- Investigate: disern details others might miss [in] an overgrown area
- Medicine: ability to treat illnesses and wounds with medicinal plants
- Nature/Survival: in the wild, identify plants and sources of food
- Identify Plants: with a quick inspection of their appearance and smell
- Activities: Find plants (DC15); Identify poison (DC20)
POISONER'S KIT (XGE pg 83)
... allows you to apply poisons and create them from various materials; helps you treat them.
- Components: glass vials, mortar & pestle, chemicals, glass stirring rod
- History: recall facts about infamous poisonings
- Investigation/Perception. inspect poisoned objects or try to extract clues from events that involve poison
- Medicine: treat victims of poison; Insight into how to provide the best care
- Nature/Survival: Determine which plants and animals are poisonous
- Handle (and Apply) Poison without risk of exposing yourself to its effects
- Activities: Spot a poisoned object (DC10); Determine a poison's effects (DC20)
Each Tool Proficiency discusses working with very specific things for very specific purposes:
- Alchemy: use "chemicals" and "substances" like salt, iron, purified water, or acid, to do things like creating specific "concoctions" (potions of utility), using those chemicals and substances.
- Herbalism: use "medicinal plants and herbs" to do things related to creating "healing potions" and treating illness, using medicinal plants.
- Poisoner: use "poisons", "substances", "chemicals", and "materials" (pertaining to poison); handling "plants" and "animals" that are poisonous; to create, treat, or apply poisons.
Alchemists can identify poison fairly easily (DC 10). Herbalists can also identify poison, but with much more difficulty (DC 20). But there's no DC for a Poisoner to do so, because for them it is trivial, no roll required or difficulty involved. Most importantly, only a Poisoner is trained to do any of this SAFELY. A doctor can diagnose luekemia, but an oncologist knows much more about how to prevent, treat, and manage it.
As always, though, ask your DM. They'll decide if you can even try it, and how difficult, dangerous, effective the attempt can be. But the rulebooks don’t indicate such an attempt being successful otherwise. If they allow, it will likely be exceptionally difficult. It will also be dangerous, almost certain to fail, and probably have the potential to foul or damage the kit in the attempt (grinding herbs to lay on a wound in the same mortar & pestle previously used to mix aneurotoxin, or trying to put a healing potion in the same vial that previously held snake venom, etc.).
Long-Winded Answer: Probably no, ask your DM
An Alchemist know how to work with basic, fundamental things, like acids, fire, smoke, water, stone, charcoal, etc. In modern terms, a Chemist. They make "useful concoctions" (potions with specific utility), not healing or magical ones. They can rather easily identify a poison or potion, but are not proficient in creating all potions or any poison. They might know that a poison involves chemicals X, Y, and Z, but not how or where to best find them or how it was adminstered.
An Herbalist knows how to use medicinal plants and herbs for healing. They make potions and salves that heal or treat injury or illness. In modern terms, a Botanist or Healer. They can, with some difficulty, identify a poison, even know what a certain poison does, but not what it's made of, or how to do harm. They might know that a poison causes this or that pattern of necrosis or rash, but not where it comes from, how to isolate it, or whether it was natural or manufactured.
A Poisoner knows specific knowledge about how to gather, create, recognize, or treat poisons specifically. This includes some plants, yes, substances and chemicals too, but in the frame of how they relate to poison. They can identify a poison with little more than a cursory examination, their knowledgeable makes such deterimination almost trivial. They have the tools and training to collect toxins and venoms, increase toxicity and potency, combine them for particular effects, how to apply and administer them, as well as extensive knowledge and training in their history and how to safely handle, neutralize, and treat them.
They can tell how poison was administered, if natural or crafted, ingredients and where to find them, their rarity and/or cost. They can determine a poison is a unique coctail used by a specific Guild thought destroyed a century ago. And they will be better at treating poisoned victims... if they want to. They can also make an otherwise treatable poisoning lethal, and an Herbalist or Alchemist wouldn't be able to tell. A Poisoner is trained for all of this, while an Herbalist can do little more than identify and possibly treat these poisons. They certainly don't know enough to isolate, reproduce, or create more
Proficiency in a Tool Kit does not imply proficiency in every related Skill, neither do related Skills add up to a Proficiency:
- a Fighter is lethal with a sword, but has to seek out a smith to craft or repair one
- a Ranger knows exactly where an herb grows, but not how to weaponize it or use it as effectively as an Herbalist
- an *Alchemist might know an herb contains a chemical, but not what it looks like or where it grows.
- a Poisoner might know how to treat a sickness, but not how to cast a spells to cause it.
To answer your question, no, Herbalism Kit proficiency does not grant imply knowledge of poisonous plants, animals, or substances, only medicinal plants and herbs. Our Herbalist can identify a plant with a cursory examination, point out a poisonous vine about to be stepped on, and some symptoms a poison causes, but not how to safely or reliably find, extract, isolate, administer, or even treat said poison. It's not just the tools that matter, it's the specific knowledge, history, practice, and expertise that comes with being trained in their use. Without the Nature Skill, for example, they've no clue where to begin to look for it in the wild.
Alchemists, Herbalists, or Poisoners could possibly attempt (ATTEMPT) to do what the others could, but without any bonuses the correct training, experience, knowledge, or tools. They wouldn't know where to get the right ingredients, or how to gather them. And not at all safely, effectively, or without contaminating or destroying their equipment. This would, of course, depend on your DM, and if you can make a convincing case for at least a passing familiarity with the process: "My brother, at the monestary? He was a ninja... (also my dad's a king and I know karate)". (roll Deception)
So, could our Herbalist create a poison? Possibly. They've a better shot than somebody who can't tell a potted plant from a painting. But Herbalism Kit proficiency doesn't cover poisonous plants, how to safely handle every plants, how to combine, mix, or administer them to cause harm. Their tools don't include multiple glass beakers or stirring rods needed to isolate, concentrate, or amplify toxicity, or how to safely neutralize and sterilize their equipment if they did manage to create a poison.
Of the many plants they do know, they only know the specifics of any medicinal, beneficial, or healing properties, because that's what their training involves. An Herbalist without Poisoner training might try to create a few drops of odorless venom, but instead make something harmless, that looks like a chewed-up wad of moss and that stinks of bogwater. They are more likely to give someone a bellyache than a heart attack.
Maybe you do manage to get someone sick, but it won't be as potent (or discreet) as what a Poisoner could do. And our Herbalist is just as likely to end up poisoning themselves in the process, damaging, tainting, or poisoning their equipment, or making a mistake (like clumsily dropping a substance into a goblet which is only poisonous if injected, and anyone with any decent Perception will notice a floating blob of muck and probably retaliate).
Bottom line: If you wanna make poisons, learn proficiency with a Poisoner's Kit, or find someone else who already has it.