While this isn't exactly what you want to hear, i'd really suggest moving to W2012 and WSUS 6.3.x.x
W2012 will properly update W10 clients (if needed) and WSUS 3 isn't supported anymore (or will be desupported here quickly).
notes about WSUS 3 deprecation... (the article calls the new WSUS v4 while I call it v6 because of the internal version numbering in the product)
To your question about whether or not the DB still holds the status of files... It does...
In fact, the tbFileDownloadProgress table has the pending download files listed, and their current progress... It's not as easy as just listing the files from that table, however, and in fact I haven't 100% figured out exactly what all SQL joins are needed to get the data to look presentable but it helps you see what it's currently looking for.
Another FYI.. WSUS 6 and WSUS 3 use basically the exact same DB Schema.. I.e. some pretty heavy SQL queries developed for WSUS 3 still work for WSUS 6.
I can say that I haven't ever run an air-gapped server before, so I can't help much in that arena, but if the server can't see the files you've downloaded, it's possible an issue with where the files are stored versus where the server is looking for them... possibly a permissions issue... or something else I can't think of off the top of my head at the moment...
Is this a new development in an old server implementation? or a new install? I saw you reinstalled, just wanted to validate how long this was running previously.