[filoleg]

Yes and no. PS2 was compatible with PS1, but only the first batch of PS3 consoles was compatible with PS2 (as you said, they quite literally just built-in a PS2 chip inside a PS3). After that first initial batch, Sony stopped including the PS2 chip inside a PS3, so PS2 backwards compatibility was pretty much dead. And yeah, the lack of backwards compatibility was almost certainly due to the Cell chip architecture.

So yeah, as you pointed out, for Sony it seems like their compatibility goes a bit further into the pre-PS3 era, but for other console makers it wasn't quite the case. Couldn't play original Xbox games on Xbox360 (there is a list of like a dozen games that are backwards compatible, and even then there are issues with some of them like framerate), and neither could you do that with Nintendo/Sega consoles. In that sense, Sony was a bit of an outlier in that they came early to the backwards compatibility game. But these days, 2 out of 3 major console manufacturers pretty much standardized backwards compatibility as a simple "plug and play" feature.