If you use the steam version & log in to the same account they should (though I’ve not tested) but the windows & linux game files are saved in different locations (in the save sub folder of the following:
it does if Steam Cloud is actiavated, but it just works for saves files as of the time i tested it last, lootfilter must be copied manually.
also sometimes Steam Cloud can be a bit clunky, i already had problems with its reliability but if you can mount your windows partitions in linux (ntfs-3g/-progs etc, not sure if mint already has it pre-installed) its easier to keep the saves in sync manually (but then disable cloud save and use munually backup from time to time to avoid data loss).
Thanks for the assist everyone. i wasn’t planning on using steam to play the game (and i haven’t been) but I have a steam account, so i could look at doing that.
Just moving the files over sounds like it would be pretty easy, or at least easy to try (i seem to remember that worked for grim dawn too).