[TASK] Cleanups for sysext belog

* Fix references to old classes
* Use property injection where possible

Resolves: #44744
Releases: 6.1, 6.0
Change-Id: I3076f48876fdc7566e85810eaf22aaa87d5c71e8
Reviewed-on: https://review.typo3.org/17670
Reviewed-by: Christian Kuhn
Tested-by: Christian Kuhn