PKHeX actually does not work on Wine out of the box, it's one of those programs that are esoteric enough to not run on Wine even with today's advancements. You need to do some tricks to get it working - namely installing an old build from late 2018 and manually install .NET Desktop Runtime 7 without using winetricks.
Assuming you actually had trouble getting PKHeX to work on Wine, thankfully I managed to get it working! (Well, okay, I followed some instructions someone on Reddit posted long ago lol)
Basically, you need to install an old build of PKHeX (22.12.18, you can download it here: https://projectpokemon.org/home/files/file/1-pkhex/?changelog=6855), and manually install .NET Desktop Runtime 7 (i.e. not from winetricks, but from the actual Microsoft page). It will then work normally, even if you do the trick of renaming it to PKHaX. Hope this helps!