Ensure there's a mechanism for disabling creation of new templates

[mtias]

It's important to account for scenarios where new template creation should be disabled and only editing of those already provided by the theme / site should be available.

[carlomanf]

This looks similar to #27597, but should be more easily solved than that one. This one should just require explicitly setting $args['capabilities']['create_posts'] for the post type (or adding a filter to let other developers do it), and updating the UI to check for that capability.