xbox controllers wireless should be native
that or when its plugged in it should find the drivers or ask during the install of cachyos if you would like to install controller drivers for both xinput, dinput, and wireless dongle/windows 10 adapter
my take :
just because it's not windows, it's not like we should include microsoft driver in linux (do note i’m not representative of CachyOS 
)
anyway, first welcome to the forum, as for the how to
i do find a guide for this (not tested by me, since i didn’t own the device)
but it was worth the shot
https://www.nite07.com/en/posts/linux-xbox-controller/
if we have started to include things like nividia/amd drivers we can include microsoft xinput drivers.
its not that its hard i had to install xone but why would i know i named that when its an xbox wireless adapter and looking up on google didnt really help me understand what the i needed it for it to work that being said i think cachyos should come with every controller regardless of it being steam Microsoft sony nintendo third party i think they should just all work out of box or ask if you would like to install those things with the os in case people dont game and want minimalist route