Fan translation of The Witcher and in-game text???

Hello everyone, this is my first day on reddit and I don’t know how to use it, and I’m also writing through a translator, so I apologize in advance for possibly unclear wording.

I'm writing a term paper about in-game books in the game series and I found something in The Witcher that I can't figure out.

In the first and third parts there is an in-game book "Ballads" (https://witcher.fandom.com/wiki/Ballads), in which Dandelion's ballad "Winter" is recorded. The same ballad in two games, but in two translation versions.

I thought that in the first game they used a book translation by David French, and in the third the localizers translated it from Polish themselves and that’s almost what happened. BUT.

In the first part they actually took the same version of the translation as in the books, but everything I found referred to this translation, which is marked as a fan translation: https://bookreadfree.com/338526/8332807

I found the official translation from David French, but it is not the one used in the game. Why did they use a fan version in the game?