I recently bought streets of rage 4 on GOG with the Mr. X Nightmare DLC. I'd been playing on gamepass for PC, but didn't want to buy the dlc there since I wouldn't own the base game. Is there a way to import my save data from the gamepass version to my new copy on GOG?

I can't say for certainty, but given they're both PC versions, the question is whether or not the save is stored locally or with onedrive or something like that. I don't use gamepass, but i'd try to find where the save is stored. Some games, you just immediately start them up and the save is automatically found, 'cause they store in the same place.