So, I followed your advice and used the sources (6.3-rc6). Compiled even two versions: with my config (cf. head letter) and the Arch Linux one (I'm using Gentoo, but it still fits well), both updated with `olddefconfig`. Just to make sure that the problem is independent from the config.
Good news: I experienced the hanging 3 times with both kernels yesterday.
Two of them were on the custom kernel, and they were of the rare kind - they occured on shutdown. It goes normally, init disables the services, unmounts the filesystems, turns off the screen, but then - no response and the LED and the fan are still on. Another couple of shutdowns went normal, so the issue it still irregular.
One happened later on the Arch-based one and after a suspend.
/var/log/kern.log showed nothing specific in all cases.
Bad news: it seems, the fix hasn't arrived yet.
How do I proceed next?
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P.S. On the `pci=nomsi` case: I don't consider it being related to the issue we're discussing. For me it seems like a hardware issue that can be bypassed by reconfiguration.