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.