"Found # remote files that are not recorded in local storage, please run repair" using NAS as destination

Don’t manage the databases in AppData directly either, e.g. restoring them from some other backup.
You’ll get stale records which will be surprised at seeing new files that are not recorded in an old DB.
The logs, BTW, are in the databases, so new info may be missing, if post-format restores were done.

While I’d like to know an exact chronology of events if possible, starting NAS backup fresh may work.

Unfortunately the summary of cause behind the line shown is on the second line, which is not shown.
Until that issue is fixed, About → Show log → Live → Warning and clicking on them can get the data.

Some of them can be guessed at, for example lockfiles likely need VSS snapshots turned on as well.

A re-do might also be a good time to raise the blocksize to limit backup blocks to around a million, to improve performance. Default 100 KB is OK for 100 GB backup, but the file count suggests it’s more.

If running as Administrator is awkward to arrange, you can instead run as a Windows service, but it’s slightly complicated to set up. Note it’s easier to set up before first backup than to migrate an existing.