Hey, you’re playing a game from almost 30 years ago!
The data is actually exactly the same as what would be on a cartridge. The same way you can use a .gb file from the 90s, you can use a .sav file from the 90s too. Emulators were made to read those original files, not the other way around. Every GB emulator should have no problem reading those files.
Now save states is where you’ll run into trouble. Those are unique to the emulators, since the consoles never had them, meaning each emulator had to create them from scratch. You might find some cross compatibility, but generally not, I’d think.
This should generally be true for most emulators. And for most consoles themselves, actually – you could run most ROMs from a console and even .sav files between emulators and consoles! (e.g., with an EverDrive)