My doc team has several Mac Minis on order but they are 16GB/2TB versions so they won't be shipped until late Dec. The base models are available now.
I know Tom knows this but a kernel panic is almost never the fault of the application layer or codec. It typically is an underlying system bug which is uncovered by a permissible operation in the app layer.
The first diagnostic step I'd recommend is running the below command from terminal and evaluating what kernel extensions are in place. I think Big Sur deprecated some yet allowed others. Not sure what the behavior is. Also suggest evaluating any common hardware such as external hard drives, hubs, etc.
I'd also suggest saving each kernel panic to a .txt file and emailing it to yourself. They may also be located in /library/logs/DiagnosticReports, but if the machine is swapped you lose that. In some cases the logs are in binary format and require conversion to text using spindump -i.
The exact codec used by the A7III is probably 100 mbps 4k 8-bit 4:2:0 XAVC-S. It is a Long GOP H.264 codec common to all Sony Alpha cameras. I would be shocked if there was a generic problem with FCPX using that codec on an Apple Silicon machine, since it is so pervasive.
That said on my iMac Pro on Nov 28 I had FCPX 10.5 crash on MacOS 10.15.7 when editing Sony A7SIII 280 mbps UHD 4k/23.98 Sony XAVC-I 10-bit 4:2:2 when I added the CoreMelt Lock-n-Load plugin. This resulted in MacOS UI hang, so I made a SSH remote session from another machine and commanded a remote shutdown using the terminal command "sudo shutdown -h now". The target iMac Pro apparently shut down but upon restart reported a kernel panic, possibly due to a shutdown stall.
The key line in the panic report was "panic(cpu 2 caller 0xffffff7f93e50ad5): userspace watchdog timeout: no successful checkins from com.apple.WindowServer in 120 seconds"
The FCPX crash backtrace is below. This was on an iMac Pro so it can't be related to Apple Silicon. I've had previous problems with a normal shutdown causing a shutdown stall culminating in a kernel panic on restart, possibly due to various OWC Thunderbolt arrays or SoftRAID.