Document in "Read-only" mode all the time

I experienced this same problem (everything opened in read-only mode) and after I tried all the tips and tricks I  could find, this is the only one that worked for me: I stopped syncing the document library. 

I re-synced the document library, and now the status of the files is clearly "read only":

I have never seen this "read-only" status before and I just cannot figure out why these files are locked while other libraries are just fine. 

The only difference between the files is that the locked files are from a communication site and the files that work okay are from team sites. Otherwise the settings are the same and I have full ownership to all of them.

Ugh. This drives me crazy.