[TASK] Remove unused variable in AbstractItemProvider

After the removal of the fourth parameter of the
checkAuthMode method, the local variable $authMode
has not been removed, too.

In addition, the @todo is removed, as it is resolved
now.

Resolves: #97294
Related: #97265
Releases: main
Change-Id: I0712927a8d414e9d16b4ac89f505fa7da7c81494
Reviewed-on: https://review.typo3.org/c/Packages/TYPO3.CMS/+/74168


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