I am using LibreOffice 7.1.4.2 on a Mac. The program refuses to save a PDF document. I tried Save, Save As, and quitting the application. Each option results in 10-20 seconds of a spinning beach ball, but no save.
Did you provide Full Disk Access to LibreOffice.app?
Check the procedure in answer to question Unable to Save or Save As any document even in Safe Mode (and if that helps - greetings to Apple).
btw:
I tried Save, Save As, …
You can’t use Save or Save As to save a document as a PDF document. The function to save to an PDF file is in File -> Export or File -> Export As...