External trade with capitalist cultures doesn’t mean the Federation itself has internal capitalism, it’s just a necessity for getting things from cultures outside of it. All the poker on the Enterprise was almost certainly just friendly games with chips, not actual gambling. Picard himself says money doesn’t exist so it’s not like they’re getting a salary. And I can’t recall the projects and patrons you’re referencing, but that could mean someone providing non-monetary support like using their connections or social status to support the project.