[TASK] Use request object in Element Browsers + Link Browsers

The PSR-7 Request is now handed in some methods of
the Element Browser code. This is a prepatch in order
to avoid hidden dependencies, simplify abstraction
and adapt the related interfaces.

Resolves: #101610
Releases: main
Change-Id: I9a6486732a2f166c82edd46e62eb2ad0d4bbb633
Reviewed-on: https://review.typo3.org/c/Packages/TYPO3.CMS/+/80294


Tested-by: core-ci <typo3@b13.com>
Reviewed-by: Andreas Fernandez <a.fernandez@scripting-base.de>
Tested-by: Andreas Fernandez <a.fernandez@scripting-base.de>
Tested-by: Christian Kuhn <lolli@schwarzbu.ch>
Tested-by: Benni Mack <benni@typo3.org>
Reviewed-by: Christian Kuhn <lolli@schwarzbu.ch>
Reviewed-by: Benni Mack <benni@typo3.org>