Suggestion, outside of your original question, but specific to your above.
As this is a large iMac and transporting around is no easy task - via Friend, Relative, Associate or other Trusted Person with a Qualifying Apple Computer to run Big Sur ( this is the caveat - qualifying )
Have them or you download from the Apple Store a Full Version of Big Sur using the below Terminal Command Without Quotation Marks.
Suggest Copy and Paste the command to insure correct spacing.
" softwareupdate --fetch-full-installer --full-installer-version 11.7 "
This will download the Full Version of Big Sur 11.7 and will place a new application on the applications Folder of that Computer.
It Will Not Auto Launch
With a good reliable External Drive - Drag and Drop the " Install Big Sur " Application to external Drive
Get home and attached the drive to this computer.
Drag and Drop the above mentioned Application into the Applications folder of your computer
Now, you are ready to Launch the Application like any other Application and follow the prompts.
There will be several Auto Restarts along this journey until the final reboot.
Big Sur 11.7 should be presented in About this Mac.