Starship development has been funded mostly by SpaceX, not by the US government. SpaceX did win a contract for the Human Landing System, but the payouts are contingent on certain milestones, such as demonstrating in-orbit refueling. Also much of that funding goes towards developing the lunar lander version of Starship, not the Starlink version that SpaceX has been testing with. If they meet all the milestones, SpaceX could be awarded $4.4 billion for the Starship HLS program, most of which would be for crew-rated lunar landers.[1] SpaceX has already spent over $5 billion of their own money on Starship, so even the largest payout wouldn't cause the majority of the funding to be from the government.
For comparison, NASA's SLS has cost $32 billion in 2024 dollars and has an annual cost of $2.6 billion. They launched one unmanned mission in 2022, and plan to launch again no earlier than 2026.
1. https://www.usaspending.gov/award/CONT_AWD_80MSFC20C0034_800...