[TASK] Use new backend templating in ext:install

The ext:install BackendModuleController which renders
the install tool login modal now bows to the general
backend templating strategy.

Resolves: #96755
Related: #96730
Releases: main
Change-Id: Icf10c507bf3c9cf7d91b77b59a0fe4674448db28
Reviewed-on: https://review.typo3.org/c/Packages/TYPO3.CMS/+/73313


Tested-by: Nikita Hovratov <nikita.h@live.de>
Tested-by: core-ci <typo3@b13.com>
Tested-by: Stefan Bürk <stefan@buerk.tech>
Tested-by: Christian Kuhn <lolli@schwarzbu.ch>
Reviewed-by: Nikita Hovratov <nikita.h@live.de>
Reviewed-by: Stefan Bürk <stefan@buerk.tech>
Reviewed-by: Christian Kuhn <lolli@schwarzbu.ch>