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The artificer's Magical Tinkering feature says you need to hold the object in hand. Then touch an item to imbue it.
The language on how you accomplish the task is vague to the point that I suspect they kept it that way intentionally:
To use this ability, you must have thieves' tools or artisan's tools in hand. You then touch a Tiny nonmagical object as an action and give it one of the following magical properties of your choice: ...
That's it. Everything else is left up to the DM and player to work out.
It makes sense they left it vague. They don't require any particular tool, so anything works; a ladle (cook's utensils), lockpicks (thieves' tools), pens and ink (calligrapher's tools), or a beer barrel, perhaps with some barley, water and yeast (brewer's supplies), somehow. There's no way to write rules that would describe how each of those things works that makes any sense (especially given how quickly it works; the imbuing takes under six seconds to complete), so it's up to you to come up with the flavor for whichever set of tools you use; they should be involved somehow, as it feels silly to require them if they aren't involved in any way besides occupying one of your hands, but anything you and the DM can agree on works.
The "You then touch" wording officially precludes tinkering with reach derived from comically large or remotely manipulated tools. You have to touch the item to imbue, and while a DM might allow greater flexibility (e.g. I'd be inclined to let a multiclassed Arcane Trickster/Artificer tinker at a distance with their Mage Hand, given the Arcane Trickster's unique facility with thieves' tools using that spell, even though that's stretching the rules even further than the giant ladle), I wouldn't expect to be able to do it beyond your character's natural reach (typically 5').
The artificer's Magical Tinkering feature says (TCoE, p. 11):
You've learned how to invest a spark of magic into mundane objects. To use this ability, you must have thieves' tools or artisan's tools in hand. You then touch a Tiny nonmagical object as an action and give it one of the following magical properties of your choice: (...)
It only states that you need to touch the object, not that you need to touch it with the tool, so you don't need to do it with the tool. It could be with your other hand, or with a head butt.
The Artificer description advises you to use your imagination to describe how to use your tools, but that this does not have any game mechanical effect. Per the sidebar "The Magic of Artifice" (TCoE, p. 11):
As an artificer, you use tools when you cast your spells. When describing your spellcasting, think about how you're using a tool. For example, if you cast cure wounds using alchemist's supplies, you could be quickly producing a salve. If you cast it using tinker's tools, you might have a miniature mechanical spider that binds wounds. The effect of the spell is the same either way.
Such details don't limit you in any way or provide you with any benefit beyond the spell's effects. You don't have to justify how you're using tools to cast a spell. But describing your spellcasting creatively is a fun way to distinguish yourself from other spellcasters.
Because how you describe or use your tools does not provide you with any benefits, using an extra long tool should not extend your touch range for spellcasting. Magical Tinkering is not spellcasting, so ask your DM if they would apply the same logic to it, or not. I'd rule it will work the same way.
You asked about other classes. It may help to think about this by analogy: tools for the artificer work in much the same way as foci for other spellcasters. You also do not need to touch a creature with your spell focus when you cast a touch spell, you just need to touch them, and having a long staff as a focus will not increase your touch range.
The Artificer is a quirky class. If you play it as written, it has some very strange mechanics. Here, for example, it is you doing the touching, while the tool acts as a kind of material component.
But a way to make the Artificer come to life is to work with the DM and player to make the magical pseudo-technology of the Artificer make half sense.
In my experience, often this involves "magical pre-preparation". Your tool kit is one that you have modified for your own purposes, and you use that preparation to insanely quickly cause the effect to occur.
For example, if your artisans tools is a cooking tools, and you make an object glow, you might quickly squeeze out some paste from packets in your cooking tools, light the thing on fire with a spark, then remove the flame with a bellows while leaving the light intact. All as a single action.
Most of this is just flavour, but you (a) had your cooking tools, and (b) touched the object, and (c) spent an action. The object now sheds bright light in a 5 foot radius and dim light in an additional 5 feet.
Doing stuff like that - acting as if in-game you are actually doing pseudo-technological magic - often feels more fun than just saying "I hold a ladel, lick the rock with my tongue, and it starts to glow". By the rules both are equal descriptions of creating a glowing object, but I find the first one is far more fun.
Magic spells become gadgets you prepared for just this situation and barely manage to get working at the right moment. Cantrips are trustier devices you have built that work reliably, so long as you constantly and continuously repair them (whenever someone else tries to use them, they do it wrong and they don't work, to your great frustration).
With this model of Artificer, "hold" and "touch" basically means "have a free hand" and "within 5'", and you (as a player) have to avoid trying to use the fiction you invent to BS your way around game restrictions - the purpose of the fiction you invent isn't more capabilities, it is providing fun flavour for a class whose mechanics don't match the description all that well.
