[TASK] Use appropriate SQL handler class

Resolves: #56477
Releases: 6.1, 6.2

Change-Id: I3940f37d2f60566973ed900c53edc003d56a49fd
Reviewed-on: https://review.typo3.org/27979
Reviewed-by: Nico de Haen
Tested-by: Nico de Haen