This interview has some details about how it was done on Xbox: https://hanselminutes.com/632/eric-heutchy-on-backward-compatibility-xbox-one-x-enhanced-games-and-the-heutchy-method
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The hardware architecture on the PS2 and PS3 was so radically different, it effectively makes emulation impossible.
The change made in the PS4 and PS5 makes the transfer of those games relatively trivial, but attempting the replicate the now abandoned Core processor of the PS3 is the hold up there, as is the PS2 Emotion Engine.
The reason the PS3 was so expensive was including PS2 hardware to handle the backwards compatibility. They weren't going to repeat that mistake with the 4 and 5.
Meanwhile, on the Xbox side, Microsoft never had that problem.
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Sony changed their CPU architecture every time until PS4/5. The only reason some PS3s could play PS2 games is because they had also had PS2 hardware in them. Xbox has been x86 the whole time.
The 360 is IBM power pc based.
The simple answer is that microsoft is a far more advanced company in terms of programming an OS, the gap shows when you compare console securities, where virtually every nintendo or sony device had software vulnerabilities, while microsoft consoles tended to need to be hardmodded