Can report that Big Sur works great on the 4,1/5,1. Just need a newer GPU ! WiFi card needs to be updated as well.
Best way to do it is run the install on another machine that supports natively. I have done this using a TB enclosure with PCIE drive.
There are apps to make this easier. But once installed, all that is required is:
sudo nvram boot-args="-no_compat_check"
This allows normal function. If you do an NVRAM reset, you will need to reapply.