Can you run the following command (on the user account that has problems) using the version of Brave that works and the version of Brave that triggers a password prompt?
brave-browser-stable --enable-logging=stderr --vmodule=key_storage_linux=1
You should see something like:
[98785:98785:1114/120537.609487:VERBOSE1:key_storage_linux.cc(117)] Selected backend for OSCrypt: BASIC_TEXT
[98785:98785:1114/120537.609511:VERBOSE1:key_storage_linux.cc(128)] Trying to find a working backend manually.
[98785:98785:1114/120537.636016:VERBOSE1:key_storage_linux.cc(165)] OSCrypt using Libsecret as backend.
[98785:98785:1114/120537.636034:VERBOSE1:key_storage_linux.cc(128)] Successfully found a working backend: GNOME_LIBSECRET