So you bought a PS2 game digitally on your PS2 and it works on your PS4? Or did you buy a PS2 game on the PS4 digitally that was designed to work on it? It looks like you don't understand backwards compatibility. A PS2 game purchased on the PS4 digitally was a PS4 game and should work on the PS5.
It's the same with XBox BC, except you don't buy the game. You still need to download a version compiled for the One and Series. The disk only prompts a download. So by your definition XBox One and Series don't have BC at all, just free updates for lazy remasters ;p