As you already know, most of your disk space has probably been occupied by media files (Music, Photos and Video Files). You can turn iCloud OFF on your MacBook Air and then begin deleting the media files and other data that you do not need until you get some free space left so that macOS can operate efficiently. Since iCloud will be OFF, whatever you delete will not affect your other devices.
If your storage space is mostly occupied by Photos and Videos then there is another option. You can turn Optimize Mac Storage ON. Open the Photos app ➔ Preferences ➔ General: Here, put a checkmark and activate Optimize Mac Storage. This action will continue to store your photos on iCloud in Full Resolution while maintaining space saving low resolution photos on your Mac. When you view a photo on your Mac, then the Full Resolution version will downloaded and displayed at the time. The process may take a few hours depending on the size of your photos library.
Axel F.