I'm not seeing what makes SpaceX government funded beyond just that it provides services to the government? The same as any other launch provider would be doing? At this point the vast majority of SpaceX's activity, and likely cashflow, is from its mostly self-funded Starlink.
SpaceX won the original HLS contract because their design actually had hardware in testing, actually met NASA's payload, landing area and testing requirements, had a clear path to commercialization and was willing to cover most of the cost themselves, as otherwise NASA wouldn't have been able to choose anyone given the limited funding allocated by Congress.