[TASK] Use new templating strategy in EditDocumentController

Apply the new templating strategy to EditDocumentController
(FormEngine record editing) by adding a first template and
refactoring the class a bit. EditDocumentController is
still a complex beast, the patch is quite conservative
and cleans up only relatively obvious parts.

Resolves: #96787
Related: #96730
Releases: main
Change-Id: I30e340276a5687d96f04b11a567444272ec1d96c
Reviewed-on: https://review.typo3.org/c/Packages/TYPO3.CMS/+/73357


Tested-by: core-ci <typo3@b13.com>
Tested-by: Stefan Bürk <stefan@buerk.tech>
Tested-by: Benni Mack <benni@typo3.org>
Reviewed-by: Stefan Bürk <stefan@buerk.tech>
Reviewed-by: Benni Mack <benni@typo3.org>