Specifically Arch. I found a GitHub page for xbox360wirelesschatpad but the installation instructions are for Windows. I know LibUSB is available but the vjoy driver doesn't seem to be. I feel like there's probably some comparable package.
There might also be an alternative way to do this all together. There seem to be a few methods of doing this on Windows using third party applications.
I am mostly doing this for the novelty of it but I feel like it could be useful for navigating my PC from my couch or responding to messages through Steam.
It seems like this whole process is pretty plug and play with the Xbox One controller and it's chatpad but that's not what I am after.
I wonder if your K400 is defective. I have the old black & white K400r (refurbished?) and the batteries last for many months even when I forget to switch it off.