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.
Check out Playnite then. I'm not sure about cloud save, but I liked it very much on Windows.