[keyserver] Decouple processSuccessfulLogin from logInResponder

Summary:
Pull out processSuccessfulLogin from logInResponder so the logic can be reused by siweAuthResponder.

These queries are run once password/signature are validated and the user has correctly authenticated.

Test Plan:

1. Create account with password
2. Log in to ensure things work
3. Log out
4. Patch this diff in
5. Successfully able to log in again

Not a super comprehensive test plan, but it should be a pretty straightforward refactor.

Reviewers: ashoat, tomek

Reviewed By: ashoat

Differential Revision: https://phab.comm.dev/D6059