I started watching Repo numbers back around 2001 and the approach back then was that the Fed would make credit available to banks and banks would buy Treasuries. Sometime in the last decade, they started buying Treasury, and other Government securities, directly.
The Federal Reserve is actually owned by private banks but it's management is appointed by the Federal Government. So there is a distinction between the Treasury and the Federal Reserve. The Federal Reserve also aims to make profits though I believe that it turns over much of them to the US Treasury.