There are rumors of the Switch getting a successor next year. My biggest wish is for it to be compatible with the current games, included digital purchases. Honestly, if I can import my digital library and saves I’m already sold on a switch successor

Xbox has always doing the x86 architecture(Edit: as corrected by following comment, 360 was not.) so it's much easier to do BC. For Sony or Nintendo it's just not worth the effort until the emu is mature that they can just reap the benefit. PS5 can already play almost entire PS4 library, Anything PS2 or before can be emu pretty consistently if you are trying to get it done, then it only left PS3 in a weird place. For PS3, many good games already have a PS4/PS5 remaster games, for non-best sellers you can probably get a cheap ps3 slim with enough storage to play those left out games.(ie, PSN only Puppeteer), OR stream them like you mentioned.

Basically all games of note going all the way back to the OG Xbox

This interview has some details about how it was done on Xbox: https://hanselminutes.com/632/eric-heutchy-on-backward-compatibility-xbox-one-x-enhanced-games-and-the-heutchy-method

I wish that was true, there are so many games I would go back and play again. PS3 was a technical marvel for it's time, however using it was so complicated that we only got to see it's true potential by the end of it's lifecycle with games like TLOU. So just speaking of raw power, PS5 could %100 not emulate PS3 games flawlessly as we barely have PS3 emulation on PCs. Technical part aside, it just doesn't make business sense for Sony to invest in it. You also have to keep in mind if Sony offers PS3 emulation, it can't stutter or crash on some games. it needs to be a commercial grade product which is not even guaranteed with PS2 or NES emulation on PC