Just to put this not compatible theory to rest, the new https://library.playstation.com/ web site has an API which it is accessing to determine the backwards compatibility state of a game. You can see the requests it makes if you have the developer panel open in your browser.
Anyway if you put in one of the IDs used for P.T it returns a compatible result:
And to verify it's actually working as intended, if you put the ID of a known incompatible title like Hitman Go it returns not compatible:
So P.T is very much playable on the PS5 through BC as long as you have it on your PS4 and can transfer it.
Awesome detective work, someone tag this poster.