How do I trim an insanely large amount of system data?

Here is an article explaining what the system (or other) storage contains:

See used and available storage space on your Mac – Apple Support (UK)

The main problem Apple created (in my humble opinion) was to make the category inaccessible. About the only thing that might take up room there that you can do something about are Time Machine snapshots. Sometimes pruning that and restarting will greatly reduce the space being used.

https://derflounder.wordpress.com/2018/04/07/reclaiming-drive-space-by-thinning-apple-file-system-snapshot-backups/

I called Apple Support. I was told the amount of System Data on my MacBook was insane. The only way to clear it was to back up my data using Time Machine, reset my MacBook to factory settings and then reinstall data from Time Machine. My System Data went from 605 GB to 14 GB.

use one of the Utilities mentioned in this article to identify the biggest "Boat Anchors".

Then you can make a thoughtful deciosn about what should be kept.

What is “Other” storage on a Mac, and how… - Apple Community

The Finder does not easily show you what is in System Directories.

In the article I referenced, after discussing built-in methods:

... it’s often easier to use a disk management utility to identify the larger files. Personally, I use the free Disk Inventory X; another option is the free OmniDiskSweeper

There are also apps on the Mac App Store that offer similar features, such as DiskSight and Diskopolis. These apps do not distinguish what is in Other, but they will show everything taking up space on your drive and allow you to sort it by size and to find it, regardless of whether About this Mac > Storage puts it in a specific category or in Other. 

unlike automatic "Cleaner Apps" these Utilities do not keep scanning your files non-stop and deleting things willy-nilly.

You run them,

they search for a bit, then tell you about it,

then YOU decide what stays and what goes.

Then you say QUIT and they stop doing stuff.

As mentioned, DO NOT use any "Cleaning Software". Try with a restart and clean Safari and Chrome history and cache.

Just don't download any software for cleaning storage. Restart your Mac. To clear Safari and Chrome history and cache see these: Clear your browsing history in Safari on Mac - Apple Support

Clear cookies in Safari on Mac - Apple Support

https://support.google.com/chrome/answer/95589?hl=en&co=GENIE.Platform%3DDesktop#zippy=

These have helpful information, but don't pay attention to the suggested software

https://www.macworld.com/article/676493/how-to-delete-system-storage-on-mac.html

https://beebom.com/system-data-mac-storage-delete/

And finally another forum with similar problem

System data storage use on my mac is huge… - Apple Community

Disk Inventory X is spelled out and its display is shown in that article.

DO NOT use an automated cleaner program on your Mac. Ever.

They are worse that guessing, and can cripple your Mac. We see sad stories here every week.

The simple Utilities mentioned in that article will quickly identify the biggest files, and if you want help with 'what exactly is that' and 'can I safely throw it away?' Readers are eager to assist.

The ones mentioned in that article, which is from Apple discussions, has stood the test of time. No one has reported any issue with those four.

The Apps in that article do not CLEAN. They merely identify by SIZE, and let you decide (or post the filenames on the forum and readers can help).