there was an unknown error while writing metadata to this photo

I have the same problem.  And it just started after upgrading to 13

I have gotten this error a few times, and at least in my case, nothing to worry about. (I don't know if your case is more serious than that)

Some possible solutions:

1. Try again in five minutes.
2. Turn off sync with the Adobe cloud, sometimes when a file is being synced, writing metadata is prevented until the sync completes (that's my guess, anyway, seemed to work for me).
3. I also suspect in my case that there was an interaction which I cannot explain between LrC and GeoSetter (which also accesses the files), other than to say when I shut down GeoSetter the problem went away.

I have the same problem. Just changed from windows 10 to 11 on new computer tranferred my lrcat and lrcat data files to new computer and have "unknown error while writing metadata to this photo" on all photos.