It is not specific to the TRx40 for proof this link. it must be modifiable for your platform.
To do the test, I have two absolutely identical EFIs just with the difference of kext for the ethernet ports.
The first with the I210.kext (works very well with BigSur by the way)
The second with the Kext AppleIGB.kext
With the first, the Monterey system is very stable. With the second one doing...
I use a BlackMagic Design UltraStudio 4K Mini so it's an external interface connected in thunderbold 3 and every time when I switch from Windows or BigSur, I have to do a firmware update of Ultrastudio 4k mini. it is offered to me automatically.
I think we have to look on this side.
For my part when I flashed the card, I was under Catalina and in the passage to BigSur I did not have to flash with a new version.
The card is still recognized, I am currently under 11.2.3
Have you checked that you have the SSDT-TBOLT3-NVM23.aml file in the EFI / OC / ACPI folder and...