how to increase the storage in my MacBook air

Hate to Report - the SSD and everything else is Soldered to the Logicboard. Thus can not be increased. Workable option is to purchase an External Drive - USB and use it for files not required on a daily basis. These things are cheap and very portable.

What is “Other” storage on a Mac, and how can I clean it out?

OmniDiskSweeper - it is safe to download and run it. Like the previous method - it too will give a picture of what large files are on the drive.

Tips How to Upgrade to Big Sur 

There are several points to consider before attempting the upgrade to Big Sur. The most important is Due Diligence on the part of the User and is a Prerequisite for a smooth upgrade.  

The below points should all be consider Before attempting the upgrade.

Point # 1 - Are there pre-existing Unresolved Software Issues. They should be resolved prior to upgrading - many will / may carryover to Big Sur making the system unstable / unusable.

Point # 2 - Are there any AntiVirus, Disk Cleaner, Optimizers, Defrag, VPNs etc installed which should be removed as per Developers Instructions. They are useless, unneeded, cause havoc and interfere with the normal operation of the OS. The Built-in Security of Big Sur is all that is required.

Point # 3 - What are the System Requirements ie: Empty Space Requirements specific to the Big Sur.

Point # 4 - Does the intended computer qualify for the upgrade.

Point # 5 - Does the existing System File System meet the file system requirements of Big Sur. Like Catalina - Big Sur requires the drive be formatted as APFS with GUID Partition Map. It does not automatically convert HFS Journaled to APFS.

Point # 6 - Are the installed Applications / Extensions compatible with Big Sur. Check with the Developer for compatible Apps / extension or do they offer updates. Same goes for Third Party Drivers for Printer, Scanners etc.

Point # 7 - Do I have a Rescue Plan In-Place. This comprises having a Time Machine Backup and for addition purposes - two Tested Bootable Clones each to separate external drives. This is insurance incase the upgrades goes sideways

Point # 8  - to upgrade to Big Sur will require a quick, stable and reliable Internet Connection - preferred method is via Ethernet Connection. If not available and using Wifi - move computer as close to the Access Point / Router and disconnect all other devices connected to Wifi. Want the maximum bandwidth for the computer being upgraded to Big Sur.

It can be done. What version of macOS is to put on external SSD? Must mention, the version to go on External SSD will be governed by the Age of the computer you are on right Now. If computer is running say High Sierra and can Not be upgraded any higher - one can not install Mojave, Catalina or Big Sur on the external.