Can't reproduce it. 3 catalogs in a project, all entities on these catalogs. Sync -> Last sync date has all "Unknown (switched off by project setting)". Even if I switch it on first, then sync, I get the sync dates filled in properly. Then switch it off, save, close the project, reload it, then sync again, I see 'unknown (etc.)', and no date is added as a sync date.
This is with sync source set to 'database'