[TASK] Use new templating strategy in ext:form

We need to move the main templates around a bit
to apply new backend templating strategy to the
ext:form backend controllers.

Resolves: #96774
Related: #96730
Releases: main
Change-Id: I0c3f82f33c17f482a0487e3f29eb8b2ba76ff128
Reviewed-on: https://review.typo3.org/c/Packages/TYPO3.CMS/+/73338


Tested-by: core-ci <typo3@b13.com>
Tested-by: Nikita Hovratov <nikita.h@live.de>
Tested-by: Benni Mack <benni@typo3.org>
Reviewed-by: Nikita Hovratov <nikita.h@live.de>
Reviewed-by: Benni Mack <benni@typo3.org>