I have confirmed that the bug I suspected, and wrote of in the post above, is correct. The app is not acquiring edit rights to my SD card. This breaks themes, the ability to edit files, and probably several other things.
THE WORKAROUND: I moved the vault sync from my SD card to my internal storage. Now the Android app can use themes and files are editable.
This is definitely a bug regarding SD card editing rights, something that the Android app has to request. I would prefer to use my SD card but I don’t know any user-level work-around that can provide those rights. For now I’m stuck with internal storage.
I tried posting this as a bug but it was moved to the Help forum. Maybe the devs are not actively resolving Android bugs right now. Hopefully a dev will see this eventually when they start work on the Android app again.