[TASK] Put logic of fetching page content from cache into more readable format

The process of checking if
a) the page content (or parts of the page incl. instructions for uncached objects)
b) the TypoScript parsing for this set up
is available in cache via locking is now cleaned up a bit by

a) calling TemplateService (pagesection cache) with the required parameter directly (internal)
b) moving the "take cached data and move it into the TSFE properties" into a smaller
method

Resolves: #89654
Releases: master
Change-Id: I65ba3aedab38616194cbefdf7c51524a24a29643
Reviewed-on: https://review.typo3.org/c/Packages/TYPO3.CMS/+/62305


Tested-by: Susanne Moog <look@susi.dev>
Tested-by: TYPO3com <noreply@typo3.com>
Tested-by: Daniel Gorges <daniel.gorges@b13.com>
Tested-by: Benni Mack <benni@typo3.org>
Reviewed-by: Susanne Moog <look@susi.dev>
Reviewed-by: Daniel Gorges <daniel.gorges@b13.com>
Reviewed-by: Benni Mack <benni@typo3.org>