Antique Feeding Cup
It’s certainly understandable why this person thought they’d stumbled onto some sort of odd little teapot. With a handle and what appears to be a spout, this is actually a feeding cup. They were used for those that were too weak to feed themselves. The spout can almost be thought of as a straw but of course, the cup does need to be tipped.
The covered piece assures that the liquid flows towards the spout and not out, and over, the cup. A handy invention, in the past decades this cup has been replaced with lids and plastic tools which also help assure that it’s not accidentally broken. It could be a lovely addition for an antique cup collector.