The upgrade will start even if you only have 1% of free space left and will fail. You should see a pop up message showing you how much space is needed before you can attempt the upgrade again. If the installer finds that you do not have enough free space for the upgrade, it will stop and not let you continue. Quick Summary – When you start the macOS Big Sur upgrade, the installer should first check to make sure your Mac has enough free space available. Latest Updates!!! – For the latest information be sure to check the UPDATES section below. If FV2 encryption is enabled, you will be locked out of your data!
The upgrade will start, then run out of space and fail. The macOS Big Sur upgrade is not checking to make sure enough free HD space is available.