[TASK] Unify Backend Request Handlers

Due to the middleware PSR-15 concept, the AjaxRequestHandler can
be migrated easily into the generic Backend RequestHandler.

Thus, the AjaxRequestHandler is marked as deprecated.

Resolves: #83853
Releases: master
Change-Id: If7823e2bc30bdea5839a0f07e943971eeeec00c3
Reviewed-on: https://review.typo3.org/55662


Reviewed-by: Benjamin Franzke <bfr@qbus.de>
Tested-by: Benjamin Franzke <bfr@qbus.de>
Tested-by: TYPO3com <no-reply@typo3.com>
Reviewed-by: Stefan Neufeind <typo3.neufeind@speedpartner.de>
Reviewed-by: Tobi Kretschmann <tobi@tobishome.de>
Tested-by: Tobi Kretschmann <tobi@tobishome.de>
Reviewed-by: Joerg Boesche <typo3@joergboesche.de>
Tested-by: Joerg Boesche <typo3@joergboesche.de>
Reviewed-by: Susanne Moog <susanne.moog@typo3.org>
Tested-by: Susanne Moog <susanne.moog@typo3.org>