This is split out from https://github.com/matrix-org/synapse/pull/7438, which had gotten rather large.
`LoginRestServlet` has a couple helper methods, `login_submission_legacy_convert` and `login_id_thirdparty_from_phone`. They're primarily used for converting legacy user login submissions to "identifier" dicts ([see spec](https://matrix.org/docs/spec/client_server/r0.6.1#post-matrix-client-r0-login)). Identifying information such as usernames or 3PID information used to be top-level in the login body. They're now supposed to be put inside an [identifier](https://matrix.org/docs/spec/client_server/r0.6.1#identifier-types) parameter instead.
#7438's purpose is to allow using the new identifier parameter during User-Interactive Authentication, which is currently handled in AuthHandler. That's why I've moved these helper methods there. I also moved the refactoring of these method from #7438 as they're relevant.
Andrew Morgan