I used Playnite on windows back when I had Windows, it syncs with GOG and everything else.
But I find it much better to use Heroic and have one wine prefix per game. Easier to sort out compatibility and config issues.
Plus it has a beta cloud sync thing. I dont know if it uses the store’s sync system (GOG, Epic, etc) or if it’s a Heroic service on it’s own.
You could also have syncthing backup your Wine prefixes, that way you not only sync your save games, but also your whole configuration.
You could point the DynDNS to your first server, generate a valid SSL certificate with letsencrypt, then move DynDNS and the certificate to the new server.
As per your update, the problem with the server is generating certificates, right?
I use RiMusic and love it. I was using ViMusic, but then it got discontinued and I found RiMusic, which is a fork (and I like it better than the original).