A lot of stuff is in the Constitution.
A lot of Congress's powers are in the form of rules by which an executive agency can or cannot operate (through laws).
If Congress includes "and you can make some limited alterations while requesting said alterations formally under the following provisions" in every budget, that would be totally constitutional. It is no less so that they just have a law for the whole process that includes that already.
Yes, my example was related to foreign policy, but the President doesn't decide what country gets aid in what amounts by unilateral decree. Congress controls the purse. The President can name ambassadors and negotiate (but not ratify/enact) a treaty.
But Congress can also decide not to create the positions to staff a negotiating team, not provide any funds to pay salaries to them, etc.
In any case, Congress decided it wanted it this way. Congress has a mechanism for changing it. The proper attitude of the court is "this is a political issue, it has a political solution."
ETA: Only "The United States Congress" would have standing to file suit, as they are the only party to whom expenditures from the public treasury is granted, and the only party who could claim to be "harmed/injured." By their own law. That they can change.
