Wow, that's insane; as you said, I didn't even realize this leap is this vast! $5 for delivery of a bottle of water is barely more expensive than DoorDash or Postmates on Earth!!
If you launched a Starship with just a single bottle of water it'd become way more than $25,000. Similarly you could make your doordash/postmates bottle of water a lot more expensive if you moved it with a semi-trailer and a team of movers.
I don’t know what laws apply on the Moon, but thanks to ITAR, Starship probably won’t be able to launch from outside the United States, which means any actual moon travel is going to be governed by US and Florida and/or Texas law. Neither of those states have legal prostitution, and while I’m not a legal expert, I suspect knowingly ferrying prostitutes to the moon might be considered a form of human trafficking. They shut down Backpage for less.
That's what makes this all so stupefyingly difficult to even begin to try to predict what will happen. We're not going through the usual window of exclusivity. We're going from [nobody can afford this, except governments - and even then only for toy missions] to ['everybody' can afford this for anything], instantly. So there's no reason that e.g. a nursing home, or anything else, on the Moon would be restricted to the super wealthy, besides demand. Obviously these industries will be being built from the ground up, and demand will likely dramatically outpace supply for the foreseeable future. But that cost imbalance would not be because of fundamental costs.
Also you left out the most fun. Who isn't going to want to go have sex in space? Either with a partner or catching some Moon Poon at a brothel? That's going to be an industry that'll have people coming by the millions, and shouldn't really require that much to get the initial infrastructure erected.
[1] - https://en.wikipedia.org/wiki/Space_launch_market_competitio...