[TASK] Streamline EXT:tstemplate controllers

This change is a pre-patch for introducing
https://review.typo3.org/c/Packages/TYPO3.CMS/+/73339

to allow to reduce the calls to $pObj
by using inheritance for all controllers
related to TypoScript parsing in "Web > Template"

Resolves: #96877
Releases: main
Change-Id: I890f3cd30f1e04d4208732dd1503dee12ada0250
Reviewed-on: https://review.typo3.org/c/Packages/TYPO3.CMS/+/73473


Tested-by: Oliver Bartsch <bo@cedev.de>
Tested-by: core-ci <typo3@b13.com>
Tested-by: Christian Kuhn <lolli@schwarzbu.ch>
Reviewed-by: Oliver Bartsch <bo@cedev.de>
Reviewed-by: Christian Kuhn <lolli@schwarzbu.ch>