I might be wrong, but I don't think "Mayor" packages come with a Villa. I think that Villas are only available at the next level -- Magistrate.
I also think that, provided the county is not overpopulated, it is unlikely that a Mayor will have a hamlet. Hamlets are unregistered (meaning they are not prebuilt) and are built by players wherever three parcels are linked, possibly because a player buys or adversely possesses three parcels, or possibly because three players get one each. (Whenever three or more of you are gathered with one name, there's a hamlet.)
I'm not even sure if mayors could get a village (which are also unregistered). As long as there are sufficient towns, I think every mayor should get a town at least -- and I have not heard that there is a shortage of towns in comparison with mayors (but that could change as people keep buying mayor, magistrate, and governor packages).
https://chroniclesofelyria.com/blog/6549/DJ-18-Kingdom--Land-Management
(OK -- rereading that journal, I think mayors might be stuck with villages and hamlets depending on how the counties are set up.)