[TASK] Move reset password logic into a separate class

Since the reset password logic does not directly relate
on the login step, just as MFA, it's now extracted into
a dedicated class. This also allows to cover it with
functional tests.

Next to some code cleanup, the reset password views do
now properly respect the common query parameters, like
`loginProvider` or `redirect`. This helps to unify the
overall authentication process UX as the user does not
longer lose these parameters in some views, while they
are kept in others.

Resolves: #93918
Releases: master
Change-Id: If7a21a1129b5289fd575ef9232c476d3c418aa36
Reviewed-on: https://review.typo3.org/c/Packages/TYPO3.CMS/+/68773


Tested-by: TYPO3com <noreply@typo3.com>
Tested-by: Jochen <rothjochen@gmail.com>
Tested-by: core-ci <typo3@b13.com>
Tested-by: Benni Mack <benni@typo3.org>
Reviewed-by: Jochen <rothjochen@gmail.com>
Reviewed-by: Benni Mack <benni@typo3.org>