For this scenario, Company A is "selling" multiple properties (bought with cash a couple months ago) to Company B. However, both companies are owned by the same person, the only difference is that Company B has a new co-owner.
Personally, I am leaning towards purchase because it is under two different entity's, not taking account of the owners, and excluding it from being a Refi.
Lastly, the home is being rented until the leases are up in a few months where then the dwelling will be used as a vacation rental on Airbnb. To myself, since this is not guaranteed & not currently an Airbnb at closing, this a dwelling. However, others may argue the other side and I was hoping to see some opinions on this aspect as well.