From the description in your original post title, this seems very similar to the problem I’ve been seeing with one of my clients: (" Client no longer connecting on local network after DB clean up? ").
In my case: the client connects to the server and establishes the necessary encryption keys after I reinstall it (the client), the server sees that the client is online, but it won’t allow it to backup anything. No solution other than the suggested action of wiping everything and reinstalling it all over again (both server and all the clients - at the same time) from scratch. Haven’t done this yet because it’ll be a lot of work, just to chase down all the portable laptop client systems from my other family members.
Pretty sure that something in the server’s DB is what’s stopping the server from actually backing up this one client - but have no idea what the DB schema is and what fields could be set wrong to cause the problem. I’ve tried running all the DB clean up scripts with no effect on this problem. Looking forward to seeing what solution you find!