I've found that installing Parallels Tools results in the Big Sur VM hanging at boot, so you might want to avoid doing that (or at least create a snapshot before trying it).
danfry
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I was able to get past the "BIErrorDomain error 3" issue in Parallels as follows:
On a real, supported Mac, run this command in Terminal:
ioreg -l | grep board-id
2. Make a note of the board ID (mine is Mac-551B86E5744E2388, for example)
3. Run this command in Terminal:
sysctl hw.model
4. Make a note of the hardware model (mine is MacBookPro14,3)
5. In the VM configuration, under Hardware -> Boot Order -> Advanced Settings -> Boot flags, enter the following (inserting the information noted above where shown):
devices.mac_hw_model="<model>"
devices.smbios.board_id="<board ID>"
That should be enough to allow the installer to proceed.