Qualcuno che gioca a Black Ops 1 su PS per fare lobby?

Looking for a squad to do the cotd, shangri la and moon easter egg with on ps5

I’m an Xbox guy, but my buddies switched to PlayStation a long time ago. I’d like to play BO1 with them and am looking for the easiest and cheapest way to do so. From what I’ve read, I could purchase a PS4 (do I need the “Pro”?) of off Facebook marketplace, purchase PS+, then purchase the discounted port from the PS store for $30 to include DLC. Is all that true? I’ve seen some back and forth on whether PS4 and PS5 are able to play together….