A billionaire is about to [re-]become the unfettered god-king of Amerikkka (this time with more kakistocracy!!), I wouldn’t take that (current && temporary) barrier as a blocker to innovation. Get a rough prototype together now and you may corner the market while we’re still here.
> catalog of rare antique pieces or collections
Solutions already exist for a small and well-serviced market; owners of such pieces and collections already know who to fan out to and actively do, that’s why Sotheby’s etc exist.
> something that connects them with people of the same social status
See PoNeWo and PoNePo mentioned previously.
Assume that, if it’s buyable by the wealthy they already have an app for that — or, rather, their personal assistant, concierge, secretary, congressional page, rent[boy|girl] has an app for that — what you need to think about is opportunities for experiences they cannot (currently) buy.
Which brings us full circle to progressively more dangerous games.