[BUGFIX] Remove deprecation messages regarding cache manager

Usage of the global cache manager has been deprecated
in 6.2.

Clean up the usage of the cache manager and also
remove initialization code that is not needed
any more with the current caching framework.

Resolves: #57994
Change-Id: I7b93527b1df9e6d8d2e0a04aa9c8b996e0f3add6
Reviewed-on: https://review.typo3.org/29510
Reviewed-by: Georg Ringer
Tested-by: Georg Ringer