Is there a way to add a translation for every wisdom?
In assets/lang, I found only the localization of the name of the wisdom oak block itself.

You can but not easily yet. Tree text is fully client side and it's stored in jsons since it contains other info asweel. Only way to translate is to make a resource pack which replaces all those lines. To be fair not a huge issue as most lines only make sense in English so other languages can get diff ones as long as they use same names

Might just add an override in the Lang file but the English lines will stay in the jsons