System Data taking up almost the entire hard drive and will not reduce in size

If you have been dealing with this for 3+ years, just do a clean install and only import your User Data from Time Machine. I know you say this is an undesirable solution, but the time you spend tracking this down will take you much longer. It appears you currently are using Time Machine for backups. If you are using iCloud for Photos, Contacts, Passwords, Notes, Safari, etc, it will be even less data that you will need to transfer. Applications should be reinstalled manually and personally I would transfer the files I need from the Documents folder from Time Machine manually as well.

That is just the direction I would go, but others may have some specific things for you to try.

FIrst you are clearly over capacity. A 250 GB drive should never be allowed to get over 212.5 GB used. This number is a percentage that has arbitrarily been found based on a percentage of free space of 15%.

Check the root of your hard drive for iCloud and Time Machine folders. There may be temporary files from each of these tools that are eating up space. If you see those, copy them to an external hard drive before deleting them from your boot drive.

command-shift-period will reveal invisible files. If any of those files reveal services that need special temp folders, those could be your problem files that need copying to your external drive. Log files can be deleted, but not log folders.

Do not delete /tmp or any three letter folders that may become visible, as they are part of the operating system.

First, you need to know that if your computer's storage gets too full, the computer will lock up and become unusable. You don't want that. Also, you can't really mess with the system data. The best and easiest solutions to install an external disk, copy files over to it (like music, photos, etc.) then erase those files from your hard drive to clear needed space. These days external disks are reasonably priced and easily installed with vendor provided USB cables. You may have to reformat it first, using Disk Utility, however. Easy to do and problem solved.

kmosx: Installation options and their mea… - Apple Community

The option to erase everything and start over is very risky, unless you have TWO seaprate copies of all your essential data.

Thanks to cloning you can. Just make sure your clone destination on both clones is larger than the original.

This will give you a chance to clean out everything while booted from the clone that you don't need, and without getting bogged down by being too full. Make sure both clones are bootable before you erase the original.

To make it bootable you may need to run the installer of the operating system in question on top of the clone.