No it's not.Ps1 was not a digital console. But you're right about psp and psv. Most people don't know how it was in the past though and need this cleared up.
PS1 games were playable on PS3, PSP, PSV. PSP digital titles were similarly playable on PSV.
There is absolutely no reason to suspect they will separate your library into PS4 titles you bought on PS4 and PS4 titles you bought on PS5. Particularly when that's how physical works and particularly when there's a single PS store and PSN. You aren't going to buy a PS4 game on your PC and have to decide if you want to add it to your PS4 library or your PS5 library.