[lib] Factor out innerPerformAuth for use in keyserver session recovery

Summary:
We want to be able to perform a keyserver session recovery using the new identity service-based keyserver auth.

This diff factors out a new function called innerPerformAuth, which will be used within innerPerformRecovery in the next diff.

Depends on D11498

Test Plan:
Tested in combination with later diffs:

1. Set up multi-keyserver environment following Notion doc
2. Test native keyserver recovery via keyserverAuth by deleting a cookie in MariaDB console
3. Hardcode incorrect userID, try same test as 2, and confirm that it fails
4. Test web keyserver recovery in the same way as in 2
5. Test incorrect userID on web in the same way as in 3

Reviewers: tomek, inka

Reviewed By: tomek

Differential Revision: https://phab.comm.dev/D11499