This commit resolves the recurring issue where password managers
incorrectly autofill the header search bar when viewing the user
profile page.
This is achieved by wrapping the password change fields in a <form>
element, properly scoping them for browser autofill logic, and using
modern, standard `autocomplete` attributes. This addresses the root
cause of the issue, whereas previous attempts tried to mitigate the
symptom in the search bar.
Fixes requarks#2324
Closes requarks#3327