I don't know about the Xbox side of things, but ps4/5 there's an 8 minute lockout if it's not an officially license controller[1]. Ways around this are taking an official PCB from a ps4/5 controller and soldering external buttons to it. Another is getting a pcb with a usb passthru, which you can use something like a magicboot, which you load up with controller firmware/binary file, which is not an officially supported method, you're technically supposed to dump your own from an existing controller you own, but still I don't know the real legality of that all either.

1) https://gp2040-ce.info/faq/faq-console-compatibility/#why-do...

I've got an arcade stick that only works on Xbox if you daisy-chain an official controller to it. There is some kind of authentication passthrough required.