The "update" volume is where macOS stages the new OS patches (aka updates) including new major versions of macOS. At some point the contents of the update volume will be the main system volume. Basically there are two macOS system volumes these days....the one you are currently booted from & using and another one which is being staged for the next update. I've never really paid attention to the low level details of how this works exactly, but once the new staged system is ready to be used, macOS may just swap them so the "update" volume retains the older system volume until the next update is installed. I have seen the "Update" volume be anywhere between 11GB to 15GB in size on average. Does not surprise me at all.
FYI, a 120GB SSD (that is what you actually have for storage with the 128GB Apple SSD) is really too small for storing more than just simple documents and a few pictures. It is embarrassing that Apple readily sold a laptop with a 120GB SSD for so long.
If 15GB of storage is a lot to you, then maybe you should consider upgrading the SSD with a larger third party OWC SSD which is a drop in replacement for the MBAir 2017.
https://eshop.macsales.com/shop/ssd/owc
You should always have at least 20GB+ free at all times for the normal operation of macOS since even 20GB can disappear quickly. Also, you need 20GB+ of Free space which is different from "Available"...macOS makes this very confusing. Check Disk Utility to get the "Free" space value. If you completely run out of free space on an APFS volume, then most likely you will need to perform a clean install since it is impossible to delete files from an APFS volume which has no free space left due to how the APFS file system works (unless Apple has built in a safety buffer which I'm not aware of).