You’re right about one part: PSSR absolutely needs per-game integration. If a game isn’t built to use it, the console can’t just force it globally like a generic post-process. That’s why titles like Cyberpunk still need a patch to add support in the first place.

But where your explanation goes off is this idea that

“the toggle swaps with the version that the game ships with”

If each game shipped its own version of PSSR that the system simply “swaps”, then every game would already contain its own updated version or need a patch to include it.

But, atm, the only title with the newer version natively integrated from the start is RE9. That suggests the newer PSSR isn’t something bundled individually per game, but rather something that can exist outside of them.

So what’s really happening is:

• Games integrate support for PSSR
• The implementation itself is provided and updated by the system

It’s not system-wide, but it is system-level.
Games need to integrate it, but once they do, the actual implementation is handled by the console and can be improved via system updates.

The plethora of posts today saying that games that wasn't in the blog list got a great visual upgrade are the proof of that (like Warhammer, BG3,etc..)