The judge is wrong. Yes the power of the purse belongs to Congress to appropriate money. The president is not required to spend money they appropriate
Arguable. The president also cannot impound funds.
However, the executition rate can be decreased administratively at the agency level.
Actually, the administration IS required to spend the money they appropriate if Congress passes a law saying the administration must spend it. But what is deeply concerning (this is a Republican-dominated circuit, by the way) is
1) that we’re talking about grants for fighting crime...
2) after Congress did explicitly ban sanctuary cities...
3) and the court is arguing on the failure of Congress to pass laws preventing funds from going to sanctuary cities, as if the inability to act represents legislative intent equivalent to the affirmatively passing laws.