Why doesn't Xbox didn't have a Xbox 360 Menu application on Xbox One and Series X|S?

Here’s the short version

It is relatively easy for CISC processor like X1/Seriesto go to RISC, but computationally difficult to go the other way to RISC (Reduced InstrucCion Set)

A top end enthusiast PC has a good leg up on Series X cannot emulate a 360 in real time

The games are run through a complex translation program and then bugs are manually squashed. You’re playing an Xbox one/series version of that 360 game, the most literal port you can possibly do. That’s why the game must always be downloaded even if you have the disc.

If you wish to read a mildly complex book on the design of 360 CPU, check out The Race for a New Game Machine by David Shippy who headed up the team for IBM. You’ll learn a heck of a lot about how they work if you’re so inclined.

GPU and cpu are based on rdna 2 and threadripper zen 2s on the series x

Where xbox one uses 3 amd jaguar cores

While the first part about the IBM PowerPC processor in the 360 is correct, the rest of what you've put isn't quite right.

The Xbox One, One S and One X use an AMD Jaguar X86/64 CISC CPU with 8 cores (@ 1.75GHz and 2.3GHz). Series X and S use an 8 core 16 thread AMD Zen2 processor (Not Threadripper) @ 3.8 GHz (3.6GHz on Series S) While the graphics hardware is RDN2.

Of course, I didn't include any of this technical jargon in my original reply simply because it seemed to me the OP may not be technically minded. Not that there is anything wrong with that of course.

GameCube, Wii and WiiU also utilise PowerPC based processors.

As the systems/hardware are different it only depends on the game developer to make the game backwards compatible.

Actually developers take no active part in the programming of BC. All the 360 games made BC were worked on entirely by Microsoft's own team. The developer/publisher merely gives permission.

As the systems/hardware are different it only depends on the game developer to make the game backwards compatible.

Thank you for the response! This apply to same results from the Xbox 360 to Series X?

The Xbox 360 hardware uses a different type of CPU to both Xbox One and Series consoles.

So different in fact that to get Xbox 360 games to play on these machines takes a considerable amount of work. Each game has to be manually reprogrammed/reverse engineered. Then tested fully before release. This is why less than 600 titles are available to play. This is the same for both Xbox One and Series consoles.

Currently the BC program for Xbox 360 and original Xbox is suspended.