How to free up disk space on my MacBook

Hmm, nothing in that support article helped? What exactly did you try? ... and what happened when you did?

Here is another reference you can try:

• How to Free Up Storage Space on Your Mac - OWC

Finally, here are some steps that I use when I find any of my Macs in this state:

• Empty the Trash
• Restart the Mac in Safe Mode. Ref: Use safe mode on your Mac - Apple Support
• Scan for Large Files. There are a number of apps that can help with this, including: GrandPerspective, OmniDiskSweeper, Disk Inventory X, & DaisyDisk
• Delete 32-bit Apps and Duplicate Apps
  • System Settings > General > Storage > Applications > Delete Unsupported & Duplicate apps
• Delete macOS Installers << If any exist they will be located in the /Applications folder.
• Delete old iPhone and iPad Backups
  • System Settings > General > Storage > iOS Files
• Remove the GarageBand Sound Library
  • System Settings > General > Storage > Music Creation > nRemove GarageBand Sound Library
• Remove Opened Mail Attachements
  • Finder > Go > Go to Folder: ~/Library/Containers/com.apple.mail/Data/Library/Mail Downloads
• Remove Unwanted Podcasts
  • System Settings > General > Storage > Podcasts
• Remove Watched TV Shows and Movies
  • TV App > Downloaded > Select All > Right-click on any one, and then select Remove Download
• Remove downloaded copies of Apple Music songs.
• Remove local copies of Apple books.
  • System Settings > General > Storage > Books

The issue here may be the size of your MacBook Air's internal drive.

Just to add to previous suggestion which is suggested to be - First

Only as fall back position refer to below

Manage Storage

The final word from Apple on Managing the " System Data “ Category

System Data: Contains files that don’t fall into the categories listed here. This category primarily includes files and data used by the system, such as log files, caches, VM files, and other runtime system resources. Also included are temporary files, fonts, app support files, and plug-ins. 

You can't manage the contents of this category. The contents are managed by macOS, and the category varies in size depending on the current state of your Mac.

There are areas of the Operating System which we users have control over and that is the User Account Folder ( Home Folder )

It is generally a good computer practice to alway keep at least 20% to 25% of the Total Drive Capacity’s as Empty Space.

Allowing the computer to drop below these guidelines may eventually, cause unintended consequences including what is occurring now.

There is Purgeable Space and there is Empty Space.

Purgeable Space which is Controlled by the Operating System. When the Operating Systems decides the computer needs additional Empty Space, it will move a portion of the Purgeable to Empty space

AFAIK - there is no User Actions to hasten this transition from Purgeable to Empty Space

It can day or longer before this will occur.

The links below will assist in identifying what is taking up space on the Internal Drive and provide possible ways to remove data that is under the direct control of the User ( Home Folder ) . 

Rebuild the Spotlight index on your Mac

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

GrandPerspective 

How to delete Time Machine snapshots on your Mac.  

Often caused if the Time Machine Drive has not been attached  to the computer and TM Backup is set to run on a Schedule. 

TM Backup will make Snap Shot on the Internal Drive awaiting the TM Backup Drive to be attached. 

Only then will the Snaps Shots be transferred to the External Drive and deleted the Snapshot from Internal Drive..

View APFS snapshots in Disk Utility on Mac

See used and available storage space on your Mac

Locate backups of your iPhone, iPad, and iPod touch

If there a Suite of Adobe Applications  used on this computer ?

They may create some very large cache files that can be removed. Though, the Adobe cache files will be recreated as the Applications needs them.

https://helpx.adobe.com/ca/premiere-pro/kb/clear-cache.html

The same clearing of System Cache files can be achieved by booting into Safe Mode

They will be recreated as the System Requires

Try starting with this Apple Support article: Free up storage space - Apple Support