I have a 128 Gig Mac Mini. I was ready to give up on Big Sur after seeing how much free space I needed to free up. Here's how I made the space available.
Copy the Big Sur installer to a removable drive and remove it from your startup drive.
Run the installer to see how much more space you need.
Follow Apple instructions to offload Music and Photos libraries to a removable drive.
If you are a developer, you probably have a huge Developer folder in your user library. Copy it to a removable drive and remove it temporarily.
These steps worked for me and I was able to upgrade to Big Sur. The installer seemed to do a very good job of cleaning up OS X folders because I had 50 GB available after the install. Plenty of space to copy the Developer folder back to the startup drive.