[TASK] Use new backend templating in ext:tstemplate

A rather straight refactoring of the ext:tstemplate
"entry" controller to use the new backend templating
strategy.

Resolves: #96771
Related: #96730
Releases: main
Change-Id: Ia452ee9a88232ee5cce4e463f13c866b8c2e31ad
Reviewed-on: https://review.typo3.org/c/Packages/TYPO3.CMS/+/73334


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