So, this article describes the sequence of events as the Trump administration attempting to replace the librarian of congress, and Trump's named replacement saying he was replacing the Copyright Register with a Trump DOJ person.
I am not a lawyer but I thought it was pretty well established that (a) the library of congress is part of the legislature, not an executive branch office and (b) that the president can remove some people but can't install people in the other branches without confirmation (e.g. when a SCOTUS justice dies or retires, the president can't name a temporary justice).
https://www.govtrack.us/posts/503/2025-05-13_president-trump...