Okay, I traced TagWriter and it uses the straight 32 bit value that’s entered in hex in the app. No problems there. I locked and unlocked a tag many times with it, and the trace always shows the password exactly as I entered it.
HOWEVER!
I used the Dangerous NFC app to lock the tag with the password ABCD (so, in theory, 0x41424344 right?) and now I’m locked out. TagWriter says the tag is password-protected, and the trace shows the reader does a HALT right after TagWriter serves it 0x41424344 as a password.