[TASK] Restructured linkbrowser HTML

Restructured the HTML arround the form field in the element/link browser
to be more in line with the rest of the BE.

Resolves: #71840
Releases: master
Change-Id: Icbfc9b6c30e974f15e64d93cf327e05c2574525c
Reviewed-on: https://review.typo3.org/45210


Reviewed-by: Michiel Roos <michiel@maxserv.com>
Tested-by: Michiel Roos <michiel@maxserv.com>
Reviewed-by: Benni Mack <benni@typo3.org>
Tested-by: Benni Mack <benni@typo3.org>