Game Input MultipleXer

There problems with gamepads 4.x firmware. So, can I buy cheap china Xbox one compatible wired gamepad? Does it fit?

I don't think so. It'll be better if you can borrow one and try or return it to the store. I'm afrsid these won't have same Ids to send authentication signal.

But how xbox one s/x works with it if there is different id?

These gamepads are probably masking themselves as 3rd xbox controllers - these aren't supported in GIMX as Ids are different. You can try though, they may work if they mask themselves as normal xbox controller.

as it's hard nowadays to get hands on a gamepad with firmware < 4.x - is there anything how users may help fixing the bug somehow - providing debug logs etc?
just bought a used xbox one controller on ebay just to find out that even this is on firmware 4.8.xxx
just want to get my gimx adapter running with my Series X console somehow

It's not that simple unfortunately. Microsoft is known to change protocols between fw versions and we've already encountered this change once. We'll need to some time to find a way to make it work with gimx.

So, is there a way to emulate 3rd party gamepads like from ali? It would be a solution.

3rd party controllers works different than genuine controller. None is supported right now.