[TASK] Clean up Page Module rendering code

This change adapts various places
where there are cross-dependencies
between objects that contain state
when rendering the page module.

Resolves: #103326
Releases: main
Change-Id: I09db90bc4c47f0a15d9890ed40d6cb65b2dff30d
Reviewed-on: https://review.typo3.org/c/Packages/TYPO3.CMS/+/83313


Tested-by: core-ci <typo3@b13.com>
Tested-by: Frank Nägler <frank.naegler@typo3.com>
Tested-by: Christian Kuhn <lolli@schwarzbu.ch>
Tested-by: Benni Mack <benni@typo3.org>
Reviewed-by: Frank Nägler <frank.naegler@typo3.com>
Reviewed-by: Benni Mack <benni@typo3.org>
Reviewed-by: Christian Kuhn <lolli@schwarzbu.ch>