How to know a user can access node/{nid} and node/{nid}/latest in fastest way
If you know the route name you can check access in PHP. For the second link you can use this route:

\Drupal::service('access_manager')-&gt;checkNamedRoute('entity.node.canonical', ['node' =&gt; '1'])). 

You can find the first one with the help of the Devel module when you click on Current Route Info while displaying the content and look for [_route].

I would put the nid into the title field and override the field content in a preprocess hook. Display the link for each route if the access check returns true. Caching is no problem because caching is by default permission based.