Something is very broken ...I thought I was losing my mind. I'm having the same problems and despite scouring the internet and refining queries, over and over, couldn't find anything related until your post.
Firstly, I have had similar difficulty renaming playlists, though I've found that moving another playlist in-and-out of a folder sometimes seems to force a refresh in the interface. Very hit and miss.
Secondly, I have the same type of problem trying to rename genres. Interestingly though, the changed genres are written to the actual files and embedded in their metadata (checked in Finder), but the changes are not showing in the Apple Music browser view.
Also getting the dreaded beach-ball since the last update. Haven't had that for years.