Paper is definitely not implied as there are and were alternatives.
Fine. Parchment uses sheepskin. Papyrus needs papyrus plants. Whatever you are using - if you expect lots of books to be burned, those books must be printed on
something! Whatever they are printed on must be made in major quantities.
Paper does not imply logging either as it can be made from a variety of different plant sources.
Again - whatever you are using, you still need a lot of it to produce enough books for book burning like what is being discussed here. Whatever those are made of, there's a lot of it - there's going to be an industry around it, and the raw materials, whatever they are, must be available.
Also "books" aren't really implied either as there were and are alternatives.
Yeah, well, clay tablets don't burn worth a good gosh darn.
Sure, the book may be a folding thing, or a scroll. That's not really material to the point. It is something paper-ish and burnable, or it ain't a book-burning - it is book... sitting-in-a-fire-and-not-really-minding-it-all-that-much.
Magical equivalent is probably pretty simple to justify in a world with "Mending" spells and printing presses with Tinker Gnomes.
Wha? Tinker gnomes can make tiny clockwork toys, fire starters, or music boxes - none of those are printing presses. And mending spells fix small breaks - I don't see how those provide a library full of books.
Can the GM stipulate that printing presses (or a magical equivalent) exists in their world? Certainly! By tinker gnomes or otherwise. But that has implications.
But, that is one of those idiosyncrasies many of us envision in our Fantasy RPGs. We want the medieval Europe from our fantasies, but with magic and elves etc, but we don't want it to impact the "technology" or culture of our fantasy in other ways.
Yeah, that's my point. We are talking about Renaissance-level technology (or magical equivalent), rather than Medieval - and once you say that books can be made in large quantities, it is hard to plausibly say that *ONLY* books have been impacted by the advances. If you are up for that in your world, then there's no issue, and book burnings may make sense. If you aren't up for it, you risk implausibility.
Basically: The question isn't "can it happen" - a GM can make it happen if they want. The question is: How much anachronism or change to your game world are you willing to absorb to make this one thing happen?
Or, to put this another way - if your world is already Renaissance-level technology, then yeah, this might happen naturally. If you are still back in the Dark Ages, then you probably don't have enough books that mass book burnings would be something a power would feel a need to do. There simply wont' be enough copies of a particular manuscript to gather up to make a pile worth burning.
I mean, if in your entire barony there's only two sages who have copies of a text, does it look impressive to haul them out, with their two copies, and make a public scene of burning them? It seems... rather less than dramatic to burn two books. Kinda lame, as a show of force. Not the kind of moving symbol a despot-wannabe is going to go for, is it?