DND_Reborn
The High Aldwin
Do you realize three of your three quotes are about an "Alchemist", not Alchemy?Not true.
DMG page 139: "Common items, such as a potion of healing, can be procured from an alchemist, herbalist, or spellcaster." ~ common magic items can be made via alchemy and oils are listed under potions.
PHB page 119: "Starting at 2nd level when you select this school, you can temporarily alter the physical properties of one nonmagical object, changing it from one substance into another. You perform a special alchemical procedure on one object composed entirely of wood, stone (but not a gemstone), iron, copper, or silver, transforming it into a different one of those materials." ~ school of transmutation(magical) ability.
Xan page 48: "You were made in a vat by an alchemist." ~ under arcane origins for where sorcerer's can get their magic.
Xan page 70: "A friendly alchemist gifted you with a potion of healing or a flask of acid, as you choose."
Potions can be herbs, but can also be created alchemically.
I am sure an "Alchemist" is likely also proficient in the Herbalism kit, which is what is actually required for crafting a healing potion according to Xanathar's Guide. An "Alchemist" is also likely proficient in other tools and kits, and certainly might have some spellcasting features. I don't recall an Alchemist statblock...

Anywho, your second quote is about a "special alchemical procedure" ability granted as a class feature, it is NOT normal alchemy. It is special and done by a magical class--that is what makes that magical. Not the alchemy.
You said:
And alchemy is not used to make healing potions (Herbalism kits are used). Nor is alchemy used to make magical oils by the rules. In fact, like MOST of 5E, this point is really simply "up to the DM" as usual. The rules for crafting magical items (other than healing potions) simply state that proficiency in the required tools (or kit I would imagine?) is necessary. So, for example, how DO you craft Oil of Sharpness?? Do you need proficiency in the Alchemist kit, or Herbalist kit, or something else entirely? All the rules tell us is the CR for an appropriate creature and the costs...Alchemy in the game is how you make healing potions, magical oils and such.
You said it was used to "make healing potions, magical oils, and such." I refuted Alchemy isn't used for any of those things: according to what we have in the rules, it is used for making mundane items from the chapter on Equipment (one dose of acid, alchemist's fire, antitoxin, oil, perfume, or soap). So, for alchemy's uses in the game, that's it (as far as the written rules are concerned anyway...).To say that alchemy is not magical in any way given its uses in the game is objectively wrong.
Now, clearly (from your quotes) an AlchemIST can do more, but from what we have about Alchemy, it is not due to alchemy, but must be through some other agency.
So, given Alchemy's actual uses in the game, it isn't magical. That is not objectively wrong as you seem to subjectively believe. The only thread which might give you some hope is about crafting other magical items... Is alchemy used for those magical oils, etc.? That, unfortunately, is up to the DM.
Honestly, I would rule from my own games Alchemy would be used in that context. But even that, IMO, does not make Alchemy itself "magical", it would be part of a process... and the entire process is required for "magic" to happen.
Again Alchemists can create healing potions, but would require proficiency in the Herbalism kit to do so, which they could easily have IMO.Indeed. But you do get a pull when casting Detect Magic on a potion of healing, so where does that magic come from? Alchemists can't imbue something with magic without using magic, can they? And most games don't have magical herbs or plants.
(bold added) IME I can't think of a single D&D game (in any edition) where the DM didn't incorporate magical herbs or plants, or at least acknowledge their existence in their game.... but YMMV of course! I guess it could certainly be possible, but I would not feel personally that it would be "most games" by any stretch of the imagination.
They very well might be. We don't have a statblock for an Alchemist that I know of... Given the new trend for statblocks, an Alchemist certainly might have some spellcasting capabilities.Which to me means alchemists are some form of non-adventuring caster.
