The description for Alchemical Savant say:
You've developed masterful command of magical chemicals, enhancing the healing and damage you create through them. Whenever you cast a spell using your alchemist’s supplies as the spellcasting focus, you gain a bonus to one roll of the spell. That roll must restore hit points or be a damage roll that deals acid, fire, necrotic, or poison damage, and the bonus equals your Intelligence modifier (minimum of +1).
Now, say I have multiclassed with a Wizard and learn Infestation (a cantrip available to both Artificer and Wizard) and Chromatic Orb (only on the Wizard's spell list) via that class. Both can do poison damage so they qualify on that part.
Can I take advantage of Alchemical Savant with either spell?
Unlike a lot of other class features, it doesn't say, "When you cast an [insert class name] spell...", just cast a spell and use tools as the focus.
Initially I would just say no, but, while not laid out in the PHB, in XGE it says that the Alchemist's Supplies kit contains:
Alchemist’s supplies include two glass beakers, a metal frame to hold a beaker in place over an open flame, a glass stirring rod, a small mortar and pestle, and a pouch of common alchemical ingredients, including salt, powdered iron, and purified water.
And in the PHB, the [Wizard's Arcane] focuses are described as:
An arcane focus is a special item--an orb, a crystal, a rod, a specially constructed staff, a wand-like length of wood, or some similar item--designed to channel the power of arcane spells. A sorcerer, warlock, or wizard can use such an item as a spellcasting focus.
So it may be possible to have an arcane focus built-in to the character's alchemist’s supplies and do double duty...
The is a related question about spells with no material components, but this is about spells that have material components, but learned through a different class.