I am cautiously optimistic, I may have found a solution to the issue. By coincidence I came across
this thread that describes similar symptoms. What really caught my attention is that they mention the exact same hardware I am using (HP EliteDesk 800 G4).
Basically the issue seems to be caused by the graphics driver and its GPU power management. By disabling power management the issue goes away. I followed this advice and didn't have a crash since, two weeks and counting. More background info
here.
What you need to do is add
i915.enable_dc=0
to your kernel parameters in
/etc/kernel/cmdline
and then run
proxmox-boot-tool refresh
. After a reboot you can verify your changes took effect by checking whether the new parameter is present in
/proc/cmdline
.