I can see from the screenshot that you changed the protected memory space from only the configuration bytes to the entire user memory. You can see the AUTH0 byte now has a value of 04 which means password protect all memory pages from 04 down.
You’ll need the correct password in order to make any changes to any part of the memory. If tagwriter is not working correctly to update information on the ntag216 then it is very likely a tagwriter bug. That team does their best but there are still bugs that crop up from time to time.