Adding custom taxonomy to wp menu

The taxonomy would show up as an item in the submenu of whatever post type you register it with.

I’ve never seen a taxonomy get a top-level WP admin menu item, at least not that I can recall.

Wild guess: do you mean the navigation menu?

On the admin screen for the menus, go to ‘Screen Options’ – you should find your taxonomies there. You can activate them and add taxonomy terms to your nav menu.