Melinda Gates is trying to get the best possible settlement from her divorce. The Epstein issue is obvious leverage. Melinda loses nothing by Bill being embarassed in public, and she gains a lot at the negotiating table.
I haven't watched enough mobster movies to be sure, but I think you might have the order of operations inverted on the blackmailing process. The Don doesn't release the photos then start blackmailing, he shows you the photographs, then blackmails you, then maybe releases them if he has a reputation to keep and you didn't pay.
Some of the information is public. Who knows how much there is behind it?