how much storage is needed to upgrade from Mojave to Big sur?

It would depend if your Macbook Air hardware is a mid-2013 model or newer. If it is, you can get the standalone full installer of Big Sur 11.6.1 from the Mac App Store via the Safari browser (only), and How to get old versions of macOS. That will download into your /Applications folder, and you would quit the automatic upgrade continue prompt.

To install Big Sur on an external drive, that device would need to be previously erased in Disk Utility as an APFS (implicitly case-insensitive) drive with GUID partition type. Then, when you run the installer, you can select that drive instead of the existing startup disk for the installation target. While you have the full installer in your Applications folder, it might be an ideal time to make a bootable USB stick (>=16GB). That USB stick can be any compatible format as it will be formatted by the createinstallmedia command in that article.

If your Air is showing a Big Sur upgrade in Software Update, that will just perform the upgrade on the existing startup disk without any separate standalone installer, or the ability to shove it out to an external drive.

As of October 25, 2021, Apple is still saying 35.5 GB, though some are stating 26 GB.

How to get old versions of macOS  ie: Empty Space Requirements specific to the Big Sur. Apple states 35.6 GB Empty Space but suggest 50 GB