[TASK] Avoid AbstractDataHandlerActionTestCase

Avoiding this abstract streamlines various tests to
do more things similar as other tests.

This especially affects needed site setups, which is
now done more often based on the SiteBasedTestTrait.

There is also less class state in tests, making them
more easy to understand and follow.

Resolves: #101819
Releases: main
Change-Id: I6ad889f14da9e1a4ffe80b447c821c348e6d4b90
Reviewed-on: https://review.typo3.org/c/Packages/TYPO3.CMS/+/80815


Tested-by: Stefan Bürk <stefan@buerk.tech>
Reviewed-by: Andreas Fernandez <a.fernandez@scripting-base.de>
Tested-by: core-ci <typo3@b13.com>
Tested-by: Andreas Fernandez <a.fernandez@scripting-base.de>
Tested-by: Christian Kuhn <lolli@schwarzbu.ch>
Reviewed-by: Stefan Bürk <stefan@buerk.tech>
Reviewed-by: Christian Kuhn <lolli@schwarzbu.ch>