I can't unlock a new slot when reaching the right level that is displayed.
Instead, I have to get 1-3 level more until I can unlock it.

I use the latest build of this mod.
Mc: 1.16.3
Forge: Newest (34.1.42)

Can't seem to get this to happen, can you try see if you can get some steps to reproduce?
This could potentially happen if the trinket data is desynced so a relog might fix it but haven't had this happen yet.
Config needs to be the same on the server side and client side as well to make sure things work correctly.