"Other" taking up over HALF of my storage space
You can try Daisy Disk and it will give you a pictorial view of your drive and what is taking up space. It has a free trial so you can use it without buying it. There is also a free app called Disk Inventory X which does about the same but lists the sizes of everything it "sees". It also makes a colored map of you disk. I highly recommend you use these to scan your disk.
How can I figure out what's slowly eating my HD space? and linked: https://apple.stackexchange.com/questions/linked/5353
I find Apple's breakdown of Storage to be neither reliable nor informative.
If you're running out of space and can't explain why, then first thing to do is to boot into Safe Mode. Then Restart normally. This process may let the OS do some housekeeping, deleting temporary files and some caches.
Next, use an app like OmniDiskSweeper, or DaisyDisk. These will show you the contents of your entire drive, sorted by size. You can then dive into the biggest folder, and see what the biggest sub-folder is, and so on, until you identify what's using up the space.
Now comes the tricky part: Obviously, you can delete your own large files - documents, videos, etc; but some large files created by the OS or installed by applications may cause problems if removed, depending on what they are. So some caution and checking needs to take place.
For that reason, and others, I would not recommend using apps that claim to 'clean', 'purge', or otherwise maintain your Mac.
Also, don't try to delete Time Machine local snapshots unless the dates are more than 24 hours old.
If you're working with large video files, it's probably best to get a high-speed USB or Thunderbolt external drive and use that as a 'workspace' drive.