[BUGFIX] Do not rely on TYPO3_MODE for FE/BE checks

In order to run a subrequest in Frontend,
TYPO3_MODE kills most of the functionality.

Although it is clear, that TYPO3 Core is not 100% there
yet, some very obvious changes can actually be replaced
with simple TSFE checks instead of TYPO3_MODE.

This is only focused on rendering content (Fluid),
and this happens in FE after TSFE is initialized, for eID
scripts, this would break already.

Resolves: #88581
Releases: master, 9.5
Change-Id: I9c97da60e7df572290e54d53da5eb8dac69e8f7e
Reviewed-on: https://review.typo3.org/c/Packages/TYPO3.CMS/+/61084


Tested-by: TYPO3com <noreply@typo3.com>
Tested-by: Daniel Gorges <daniel.gorges@b13.de>
Tested-by: Daniel Goerz <daniel.goerz@posteo.de>
Reviewed-by: Alexander Schnitzler <review.typo3.org@alexanderschnitzler.de>
Reviewed-by: Daniel Gorges <daniel.gorges@b13.de>
Reviewed-by: Daniel Goerz <daniel.goerz@posteo.de>