Fix authentication failures after going halfway through a sign-in attempt (#16607)

Fix authentication failures after going halfway through a sign-in attempt (#16607)

* Add tests

* Add security-related tests

My first (unpublished) attempt at fixing the issues introduced (extremely
hard-to-exploit) security vulnerabilities, addressing them in a test.

* Fix authentication failures after going halfway through a sign-in attempt

* Refactor `authenticate_with_sign_in_token` and `authenticate_with_two_factor` to make the two authentication steps more obvious