When I turn on digest auth and do a quick GET using --digest auth (via cURL) all the endpoints are returned as expected. Try the following:
Subsequently, you should be able to query the applications in a similar manner (use digest if you've set RestInterface/AuthenticationMethod to digest):
curl --digest -u "[username]:[password]" -X GET "http://localhost:8089/api-docs"
Should return the various endpoints you would normally see without auth turned on. If this continues to *not* be the case, please send a zip file of your conf/ and logs/ to firstname.lastname@example.org. Also be sure to include the cURL requests you used in doing so and the associated responses.
curl --digest -u "[username]:[password]" -X GET --header 'Accept:application/json; charset=utf-8' http://localhost:8087/v2/servers/_defaultServer_/vhosts/_defaultVHost_/applications