Yes, you can use an AM4 cooler backplate on an AM5 motherboard.
Yes, you can use an AM4 cooler backplate on an AM5 motherboard.
B660 is an Intel chip, not compatible with an AM4 backplate. If you meant an AMD B650, those boards don't have removable backplates, so it wouldn't work either.
Ah yes, it was a typo, thanks. By backplate I mean the backplate that came with the cooler (it has an “x” shape), I wasn’t sure if using that on top of the non-removable socket backplate would cause problems long term because of extra pressure on spots that weren’t meant for that. I attached better pics in my post above