You misunderstand me, I think that we agree
If the software was programmed to run on a PS1, thinks it's running on a PS1, but is actually running on a PS2, then that would simply be backwards compatibility. Now if the software was programmed to run on a PS1, but was also programmed to detect if it was running on a PS2, and then use the improved PS2 specifications to enhance the game (I realise this is probably not realistically possible) then it would be forwards compatible.
You bring up a good point about a PS4.5 being able to improve the performance of games which weren't programmed to run on PS4.5 hardware. I guess that's theoretically possible, but I'd imagine that it would be unlikely to occur in practice without the original game getting patched to account for the new hardware. It's quite likely that things would break otherwise. Still, looking at it from the software side, software (which hadn't been patched) that thinks it's running on a PS4 would just be backwards compatible. Software which was programmed to take into account both hardware configurations would be future compatible.