Checking the PMON does not help as far as telling whether the database is in restricted mode, a long running "shutdown in progress", an archival halt or an audit space freeze.

I think that any check for the status of the database will have to be more complicated than a single test.

For example, the check on the invalid user may need to be embedded in a background job so that the test can time out in a predictable manner if the database is in an archival hang. The invalid user will not work as far as detecting restricted session mode either because the password is checked before the restricted session privilege.

Perhaps a variation on the file idea but using DBMS_JOB to schedule an activity every minute (or 10 seconds or 5 seconds depending on how up to date you want to be) that uses FILE_UTL to update a file with a timestamp and the LOGINS field from V$INSTANCE... I am not sure if they would catch everything.