The PS3 fat could only read PS2 disks because it had stripped down PS2 hardware included. It was effectively a PS2/3 combined. This was part of what drove the cost up, so they gutted that hardware from the slim.

PS4s can’t read PS3 disks because the PS3 used a bespoke PowerPC based chipset that was a colossal pain in the ass to develop for. So for the PS4 to have backwards compatibility, they would have had to either A, include PS3 hardware in the PS4 (expensive) or B, create an efficient software translation layer/built in emulator (see “pain in the ass”).

From what I have heard, they smartened up with the PS5. It’s basically just a faster PS4. At it’s core, it’s based on very similar hardware, so it’s easy to make PS4 games run without issue, but the boost in performance allows games designed specifically to take advantage of it.