Please re-read the details from Apple https://support.apple.com/en-ca/HT201475.
If upgrading from macOS Sierra or later, macOS Big Sur requires 35.5GB of available storage to upgrade. If upgrading from an earlier release, macOS Big Sur requires up to 44.5GB of available storage. To upgrade from OS X Mountain Lion, first upgrade to OS X El Capitan, then upgrade to macOS Big Sur.
The Empty Space requirements are to allow the Full Installer of Big Sur ( 12.24 GB 0 to reside on the computer and addition empty space for the Installer to Expand and only then will the Installation will commence
Another Suggest Reading Before attempting the upgrade to Big Sur
Tips How to Upgrade to Big Sur
There are several points to consider before attempting the upgrade to Big Sur. The most important is Due Diligence on the part of the User and is a Prerequisite for a smooth upgrade.
The below points should all be consider Before attempting the upgrade.
Point # 1 - There are unconfirmed reports that upgrading from earlier version of macOS will download a " Stub " of Big Sur. This " Stub " maybe about 25 MB is size and is not the Full Installer. If so, run this Application and it should pull down the remainder of Big Sur and commence the Installation
Point # 2 - Are there pre-existing Unresolved Software Issues. They should be resolved prior to upgrading - they may carryover to Big Sur making the system unstable / unusable.
Point # 3 - Are there any AntiVirus, Disk Cleaner, Optimizers, Defrag, VPNs etc installed which should be removed as per Developers Instructions. They are useless, unneeded, cause havoc and interfere with the normal operation of the OS and may even Corrupt the OS requiring a Reinstallation. The Built-in Security of Big Sur is all that is required.
Point # 4 - What are the System Requirements ie: Empty Space Requirements specific to the Big Sur.
Point # 5 - Does the intended computer qualify for the upgrade.
Point # 6 - Are the installed Applications / Extensions compatible with Big Sur. Check with the Developer for compatible Apps / extension or do they offer updates. Same goes for Third Party Drivers for Printer, Scanners etc.
Point # 7 - If upgrading from Mojave and earlier versions of macOS - Remember that Big Sur does not support anything 32 bit. These include Applications, Extensions and Drivers for any devices. There is no workaround.
Point # 8 - Do I have a Rescue Plan In-Place. This comprises having a Time Machine Backup and for addition purposes - two Tested Bootable Clones each to separate external drives. This is insurance incase the upgrades goes sideways
Point # 8 - To upgrade to Big Sur will require a quick, stable and reliable Internet Connection - preferred method is via Ethernet Connection. If not available and using Wifi - move computer as close to the Access Point / Router and disconnect all other devices connected to Wifi. Want the maximum bandwidth for the computer being upgraded to Big Sur.
Good Luck and come back to these Forums if there are questions, concerns or comments.