why is my MacBook Air 2016, with 32.74 GB available, unable to download BigSur. In fact every time I have tried, I get... you need an additional 2.65GB or some such number. Once it was measured in MB. Seriously

See the following from How to upgrade to macOS Big Sur - Apple Support

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. 

Your MacBook Air is approximately full for even your current usage given the free space reportedly available here, and an upgrade to a newer macOS version is likely to require additional storage.

macOS also doesn't run all that well with minimal free space available.

There are no storage upgrades for recent MacBook Air models, the only available approach is a newer or new Mac, or booting and using external storage. Or offloading rather more of your contents to iCloud or to external storage of course, but I'd suspect that this Mac is configured with the minimal available storage from Apple—certainly with rather less storage than what current usage expects—and that you have found there really isn't that much more you can remove.

There's no good path here, and you will be manually managing the storage for the foreseeable future.

Because you don't have enough free space on the boot drive to install it...