[TASK] Migrate AjaxDataHandler to TypeScript

Change-Id: I151598e90487811217dfa685dcb83081848f2bb6
Resolves: #82578
Releases: master
Reviewed-on: https://review.typo3.org/55908


Tested-by: TYPO3com <no-reply@typo3.com>
Reviewed-by: Wouter Wolters <typo3@wouterwolters.nl>
Reviewed-by: Frank Naegler <frank.naegler@typo3.org>
Tested-by: Frank Naegler <frank.naegler@typo3.org>
Reviewed-by: Christian Kuhn <lolli@schwarzbu.ch>
Tested-by: Christian Kuhn <lolli@schwarzbu.ch>