At first I tried to added Permissions to com_actionlogs component which worked to a point, but unless you are a Super User it ultimately doesn't work which is something I think should be changed by raising a request to remove this limitation. Actionlogs access should be managed by Joomla ACL and configurable by the site owner.
The menu option is hidden/removed by this snippet of code that says if the Menu item is in the one of these components and you are not a Super User then do not display.
..\administrator\modules\mod_menu\src\Menu\CssMenu.php
line ..388
} elseif (\in_array($item->element, ['com_config', 'com_privacy', 'com_actionlogs'], true) && !$user->authorise('core.admin')) {
// Special case for components which only allow super user access
$parent->removeChild($item);
continue;
Even if you disable line 390 there is another check that prevents the component from even starting unless you are a Super User.
If you want all Administrators to be able to see this option, and in effect become Super Users, then you can update the Global Config permission and change Super User to Allowed.
If only one or two Administrators need to be given access then you can add them to a sub group of the Super User and they will get access to com_actionlogs and everything else a Super User can access.
They will in effect be Super Users, however you CANNOT Deny their access to other components, see image below, therefore you may as well put them in the Super Group.
Seems like a logic issue in the way Joomla ACL works to me.