One thing to try is to update the firmware of the controller, however that needs to be done on Windows, the Arch Wiki has some additional info where people explain pairing issues

There’s also a section on “able to pair but no inputs” in the troubleshooting section on the same Wiki page

Not what I expected, good thing you managed to get it solved!

That dump didn’t reveal any particular useful information, however it seems like multiple people are reporting issues with mesa + segfault, e.g. https://bbs.archlinux.org/viewtopic.php?id=301550

Mesa v24.3.2-1 in Arch should revert that issue, Mesa v24.3.1 seems to be the problem one

You could check the backtrace of one of your crashes

coredumpctl debug
> bt

And then dump that trace here

It might be related to Mesa/GPU drivers