There is too much storage on my MacBook Air "System"

Rebuild the Spotlight index on your Mac

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

Free up storage space on your Mac

OmniDiskSweeper Safe to use

GrandPerspective 

How to delete Time Machine snapshots on your Mac

See used and available storage space on your Mac

The final word from Apple on Managing the " Other " Category

Other: 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.

Rebuild the Spotlight index on your Mac

If you get unexpected results when searching your Mac, rebuilding the Spotlight index might help.

Before rebuilding the Spotlight index

• Follow the steps for when Spotlight returns unexpected results.
• If you're having difficulty finding items in the Mail app, follow the steps to rebuild Mailboxes in Mail.

Rebuild the Spotlight index

1. Choose Apple menu  > System Preferences, then click Spotlight.
2. Click the Privacy tab.
3. Drag the disk or folder that you want to index again to the list of locations that Spotlight is prevented from searching. Or click the add button (+) and select the disk or folder to add.
4. 
5. You can add an item to the Privacy tab only if you have ownership permissions for that item. To learn about permissions, choose Help from the Finder menu bar, then search for “permissions.”
6. From the same list of locations, select the disk or folder that you just added. Then click the remove button (–) to remove it from the list.
7. 
8. 
   
9. Quit System Preferences. Spotlight will reindex the contents of the disk or folder. This can take some time, depending on the amount of information being indexed.

Well if the Genius Bar could not fix this issue which all the Tools and such plus having On-Hand with the machine - the Remote Help here on the ASC Forums will be even more limited.

At this point would, Suggest downloading the Application Etrecheck directly from a well Respected ASC Contributor. And Safe to use.

The application is free or paid from added features. 

Run the application with Full Disc Access ( Security & Privacy - Full Disc Access ).

It will take a Snap Shot -  both the hardware and software.

 The Report will Not Reveal Any Personal Information. 

Post back the Full Report - copy and paste - using the Additional Text Icon ( 3rd Icon to last )

We can have a look at the report for possible issues and may have possible suggestions to resolve the issues.

Any Third Party Applications that will interfere with the normal operation of the OS, alter, modify, remove or delete or attempt to do so is an invitation for disaster and may require a Reinstallation of the OS.

This includes AntiVirus, Disk Cleaners, Disk Optimizes, UnInstaller etc.

This will include CleanMyMac 

This will include BitDefender 

This will included Norton Antivirus

Sophos Av Software

Intego AntiVirus

The The Built in Security  is all that is required.