TYPO3 Core

In TYPO3\CMS\Backend\Backend\ToolbarItems\LiveSearchToolbarItem:

    public function checkAccess()
    {
        /** @var BackendModuleRepository $backendModuleRepository */
        $backendModuleRepository = GeneralUtility::makeInstance(BackendModuleRepository::class);
        /** @var \TYPO3\CMS\Backend\Domain\Model\Module\BackendModule $listModule */

        // Live search is heavily dependent on the list module and only available when that module is.
        $listModule = $backendModuleRepository->findByModuleName('web_list');
        return $listModule !== null;
    }

..... the return $listModule !== null; returns TRUE no matter if the be_user has access to web_list or not, because $listModule will be of either TRUE or FALSE :-(