How much space does a mac os update occupy after installation?

When you update the OS from one major version to the next, many of the files will be over-written by new files with the same names. Some may be deleted.

Each new OS should take roughly the same amount of space, though some may vary. Catalina didn't have 32-bit libraries, so may be smaller than Mojave; Big Sur has Universal binaries for Intel and Apple Silicon, so may be a little bit bigger.

But essentially, the amount of space should be similar. Upgrading from an earlier OS doesn't take up more space than a new install. (Apart from all your stuff, of course.)

Big Sur is 12 Gb download, according to the Apple Store. It appears that it requests around 35 Gb of free space in addition to this at installation. You should normally (i.e. all the time) keep 10-20% of the disk as free space, to allow for temporary file writing, and SSD self-management.

While installations of macOS do vary in size slightly, the previous operating system files are removed as part of the upgrade. You shouldn't expect a noticeable decrease in space available after upgrading to Big Sur.