I am not a distro hopper, but I think you’re asking the wrong question

I would keep your saves backed up and synchronized with a tool like rsync or git (not too great if they are larger sized files). It’s what most Linux users do with their config files for example.

Other solutions are having a separate partition for /home (or /Games) so that you can even distrohop without worrying about this. If the game looks for saves in a specific folder you can create a symlink (a sort of “shortcut” that tells the game to look for saves in a certain directory)

Not sure how experienced you are but I can try to explain it better if this seems suitable.