[!!!][TASK] Remove deprecated output-related code from EXT:backend

Removes and adapts some classes, methods and properties
which were marked as deprecated.

Resolves: #80705
Releases: master
Change-Id: I6f594956a4a9fcaf99345e8edc07bb31e76564ae
Reviewed-on: https://review.typo3.org/52511


Tested-by: TYPO3com <no-reply@typo3.com>
Reviewed-by: Henrik Elsner <helsner@dfau.de>
Reviewed-by: Benni Mack <benni@typo3.org>
Tested-by: Benni Mack <benni@typo3.org>
Tested-by: Susanne Moog <susanne.moog@typo3.org>