No, the market sets the interest rate. The government issues bonds to fund the government, and they have to offer an interest rate high enough to get buyers for all of the bonds they are selling.
and fed's function and policy is to follow the market: if inflation is high they increase rate, so at the end market decides through feedback loop
law, specifically Federal Reserve Act.
Why does the interest rate end up being close/near/the same as the overnight lending rate the Fed sets? Because why would anybody want any kind of risk when you can get XYZ interest rate risk free overnight short term?