Implement as the DM Pleases, It's Never Going to Make Much Sense
The Gold is the Important Part; the Materials are Abstract
The key line is that "the process takes 2 hours and costs 50 gp." It then goes on to what seems to be a much fluffier section about what this cost "represents". While arguments based on what is not said are always problematic, if actually acquiring the materials in the normal game sense was considered important it really seems that the more natural way of phrasing this rule would be something along the lines of "the process takes to hours and expends 50 gp worth of materials. These materials are...". As written, the player actually having particular barely explained inks and unnamed materials, seems to be a low priority at most.
If you want to make actual tangible materials and inks a strict necessity, that's great; it makes more sense (it's what I do). But this is hardly required or necessary, and really no different than requiring a player to come up with a background or event that supports them being able to suddenly multiclass into sorcerer, because their abruptly acquired sorcererness represents some sort of ancestral magic. This might be a logic/lore necessity, but not an actual intended mechanical constraint.
Implementation is Heavily at the DM's Discretion, as is the Whole Ability
Giving the DM particularly broad powers in this instance to construe implementation of the rule at his or her discretion is consistent with the use of the term "represents" rather than any clear language about it "expending X things" as there is for when a spell gobbles up a diamond or what have you. Saying "the wizard must first acquire X things" would also be a natural way to emphasize that yes indeed you NEED to go shopping. It does not read in such a way.
But DM discretion is also in the spirit of the spell copying ability in general, given that how much this ability can be used is entirely dependant on how plentiful the DM makes magic scrolls and spellbooks. Choosing to require actual purchase of these things is just another tool in the DM toolbox so far as doling out magic to the party's wizard goes.
As a matter of personal preference I'd very much rather the gold have to be spent on something rather than just disappear into the aether, but mechanically it seems to have been left to DMs to feel this way or otherwise, and it makes sense that it should be.
The Rule is a Conceit for the Sake of Mechanics and Balance
To me, of all constrictions on class abilities this entire need to have gold at all for spell copying is one of the most verisimilitude breaking ones, fine inks or otherwise. It is obviously designed for mechanics at the cost of in universe sense. Inks and materials are a thin justification; a pretense explained with as little detail as they could manage.
Notice that it doesn't say you must acquire or have the items (presumably then you might find them, craft them, etc), but rather that you must spend the gold. This gold correlates exactly to spell level for each and every spell. The price in the aggregate of these "fine inks" and the "material components you expend as you experiment with the spell" always follow the same cost formula despite there presumably being very different material components for different spells of the same level, as is the general lore of magic in the game. Also, normally one can cover most material components for actually casting these spells with a component pouch or arcane focus. Unless there are some strange, uniform spell-mastering-process components this really makes no sense.
The intent seems to be simply to force wizards to have to make decisions about when they copy which spells, and generally to somewhat limit their power versus other spellcasters. The lore/fluff of it is pretty stupid and illogical however you implement it, so getting hung up on inks is just a sign you should take a deep breath and step away.
Many Mechanical Conceits are Illogical
Once you think about it, realism-wise, inexplicably copying the spell without a shopping expedition makes no less sense than wizards and some other spellcasters suddenly learning particular spells at level up, or all classes suddenly gaining all manner of abilities, skills, etc. upon level up. At most tables there is no strict rule that you have to practice these things before abruptly getting good at them, but it is, of course, one of the core mechanics of the game.
At the end of the day it is a game built around mechanical conceits. It is also at the DM's discretion how to limit them. Do you let characters level up immediately upon acquiring the XP or make them wait for a rest? Do you describe the injuries characters do and receive or just talk about HP, whatever that is? How much of an explanation do you demand for what is actually being done to accomplish an investigation check or the help action?
Personally I like to put in all sorts of practices and limitations to add as much verisimilitude to this elf game as possible, for the sake of immersiveness and just feeling like the world has some sort of rules. But the designers are not mandating this, and they're not mandating you go on an ink shopping expedition.