In the database.
Exactly, but each app seems to handle them differently from Files. So, it is not well integrated afaik.
are such tags visible and editable on a synchronized file system outside of NC, e.g. in the Finder of macOS?
Nope. Support tags on all clients would at least make the database tags accessible from the desktop apps.
See many tag related requests on the github repo. Agreed that making better use of them would be awesome, whether in the database or the filesystem. Also, see this discussion on expanding projects functionality.
You’ll want to read tag usage through ~all apps for a solid idea of the discussion that has gone on for some years. 