System data taking over my phone

Yesterday I received a notification saying my iPhone storage was full. I realized that I had been downloading episodes of podcasts automatically, and deleted 60 GB of episodes. A few minutes later, I received the same warning, and noticed that after deleting the podcast episodes, "system data" now uses 60GB of my 256 GB.

I deleted some large videos and pictures, and the storage used went down from 255.9 down to 251 GB. Five minutes later, back to 255.9 with the system data taking up the unused space. I deleted more, and the same thing happened again.

I did a soft reset a few times (no change) and then a factory reset. When I try to restart my phone, I'm unable to log into icloud because my phone does not have enough storage space.

It now shows the iOS taking up its space and other small amounts of storage, and the system data taking up the entire rest of the storage space - about 240 GB.

What's going on? What next?