Got it solved.
Apparently there is a bug in iOS 13.6 that causes the system to keep its cache, instead of emptying it when it doesn't need it anymore. As a result, the "Other System Data" fills up anytime you do anything with the phone. Deleting apps, photos, videos, etc. does not help because it just goes into the "Other System Data", even if you go to deleted items and delete permanently.
The "easy" fix is to update to iOS 13.61, but a full phone will not update, even if you try to update from a computer (updating from a computer still requires 930MB of free space on the phone).
So you have to back up your phone first, then erase the phone, then restore from the backup, then update to iOS13.61 before you do anything else: https://support.apple.com/en-us/HT211686
And there was one other glitch in the mess - my iPhone had been backed up encrypted to iTunes, but the password my iPhone had for the encryption was not the one I had written down. So I had to reset the phone settings (without erasing the phone) first to allow me to make a new encrypted backup with a password that I knew. https://support.apple.com/en-us/HT205220
Whew. 3 Hours later, I got it updated to iOS13.61, and some of my settings restored. Will need to spend more time later to get all the settings like I had them.