OverlayFS does write, but it only writes “edits” in RAM. It works if you have enough RAM, and don’t need the content after a reboot (the original filesystem is read-only).
This is normal for all computers other than special synchronous devices.
What you are running into is a limitation of the “journal” size in a journaling filesystem. For a more details explanation, see:
https://forums.developer.nvidia.com/t/tuning-linux-on-jetson-nano-for-better-data-reliability-in-power-failure-scenario/252664/5
Note that something to pay attention to while reading is that lost data is not the same as a corrupted filesystem. Lost data is basically just truncated content, whereas corruption alters the structure of the filesystem such that any write would further destroy it. Repairs, once in that bad of a state, are manual because it is up to the end user what parts of the filesystem will be further cut out (and it can be large parts). My advice is to completely reinstall, there were so many errors that it is hard to distinguish from a failed drive.