So, does this mean that even a small catamaran is a “ship”? I like this definition and haven’t heard it before.

Surely then there is a watercraft that leans neither? What do we call that!?

A submarine.

Subs lean inward. Maybe that's why the General Dynamics division that builds submarines is called Electric Boat :-)

Das Boot... not Das Schiff...

There are U-Schiffe too, which are larger than U-Boote, but the claustrophobia element wouldn't have been as intense in the film. On the other hand, an U-Schiff would have never become unstuck from the bottom of the Mediterranean. Another example of ships getting stuck where boats don't. (If you haven't seen the movie, this likely makes zero sense.)

The foiling yachts used in this last America's Cup don't really lean (unless something goes wrong).

Sunk

A raft?