No, should work for every game with save files. I think you mean something like the account system in Destiny with internal login. That is definitely not necessary.
My last example was TMNT: Shredders Revenge. Played it on GamePass, bought it later and have all my save files. Other example: Nier: Automata, same thing. That one is no longer on Gamepass and I still have all my save files I started while playing on Gamepass
Should you buy it later the save file from the GamePass version carries over. Speaking from experience.
It’s not a different version, just a different license for the game so to speak
Isn’t that only if the game has an internal login?
No, should work for every game with save files. I think you mean something like the account system in Destiny with internal login. That is definitely not necessary.
My last example was TMNT: Shredders Revenge. Played it on GamePass, bought it later and have all my save files. Other example: Nier: Automata, same thing. That one is no longer on Gamepass and I still have all my save files I started while playing on Gamepass