System Storage taking 126GB of storage

Manage Storage

It is generally a good computer practice to alway keep at least 15% to 20% of the Total Drive Capacity’s as Empty Space.

Allowing the computer to drop below these guidelines may eventually, cause unintended consequences.

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?

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

➡️ Locate backups of your iPhone, iPad, and iPod touch. ⬅️

Notation - If the user is using a cloning software like Carbon Copy Cloner - suggest tweaking the Safety Net Feature in this software. It may be making additional Snap Shots that are not being Cloned to the Eternal Drive. If this should be the case, these Snap Shot could be using additional space on the drive 

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

The below as been basically already mentioned by Colleague @ Tesserax

Other / 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.

To add to previous contributors mention of " APFS Snapshot com.apple.os.update "

This Volume is both Sealed and Read Only Volume that can not be opened by the User nor by Third Party Applications.

The only Entity that can open and modify or alter this Volume is Apple.

That would occur when a update or UpGrade is performed.

Welcome and thank you too

As for " clear that part of the storage " - the only way I know would the Wipe the Entire Drive of everything.

Then start with a fresh installation

Notation, the exact some Drive Structure appearing in you Original Posting would be recreated.

IMHO - that would be not achieving what the user wants

As previous Contributor mentioned a Larger Capacity Drive would be required, though, that too is generally not longer possible to Swap out the drive and replace with larger drive.

Reason, the SSD is Soldered to the Logicboard

The options from Apple directly as per below does remain an alternative to get the larger capacity drive.

Just be sure to place a Built to Order with at last 1 TB Drive

Explore the Apple Trade-In  Process where the Value of the exiting device could be used against the cost of a new Apple Computer, iPhone or iPad  

Or Shop Refurbished Apple computers at an Apple Reduced Cost

Have used both previously and have been satisfied each time.

According to Apple: Other or System Data contains files that 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.

System also includes Time Machine (TM) local snapshots and those shouldn't be removed manually. However, they can be, and the simplest way to do so is to temporarily disable automatic TM backups. Leave it disabled for, at least 10-15 mins, and then, re-enable it.

You can find out how many there are by entering the following command in the Terminal app:

• sudo tmutil listlocalsnapshots /

Try as you might, you're limited in what you can store on your laptop as it have a too small capacity internal drive. I can never figure out why Apple even sells laptops with less than a 512 GB drive ... except to keep the price down to encourage more buyers.

Since you have a 256 GB drive, then 40 - 50 GBs is what you should try to keep "free." Regardless, macOS will manage that System storage category, so you will have to be diligent in keeping what you have left to work with.

Looking at the listing you provided, your laptop has a single APFS Container with a total capacity of 256 GB. Within that container, it has multiple APFS volumes. Where this System data resides in in the Macintosh HD - Data volume.

Also notice the strange volume, called: APFS Snapshot com.apple.os.update. When updating/upgrading macOS, this snapshot is created. Basically, it is a fall-back measure should an update not be successful. Again this is managed by macOS.