When I lived in the uk ‘villa’ was a popular term to describe a holiday house in a sunny overseas location with a pool.
When living in New England a villa was an older style lakeside home, I think.
Here in NZ it’s more commonly used to describe an architectural style usually from a particular time period. I was confused when I first got here why these houses were being described as villas - they are mainly in urban areas with little outside space, certainly no pool in sight. I’d never heard houses like this described as ‘villas’ anywhere else.
So I guess it depends who your market is and what they’re likely to call it? I’d lean towards your house being a villa