Congress quite literally has the power to pass laws. According to the Constitution, the President "shall take Care that the Laws be faithfully executed"; the President's oath of office requires that he execute the laws set by Congress. So for example, if Congress were to pass a silly law saying "the FBI shall spend exactly $X on computers, down to the cent", then the President would be required to make sure the FBI spent exactly $X on computers, down to the cent. The President has many powers, but "deciding not to execute the laws passed by Congress" is not one of them.

Quoting from the page you linked:

> Impoundments usually proceeded on the view that an appropriation sets a ceiling on spending for a particular purpose but typically did not mandate that all such sums be spent. According to this view, if that purpose could be accomplished by spending less than the appropriation’s total amount, there would be no impediment in law to realizing savings. Impoundments were also justified on the ground that a statute, other than the appropriation itself, authorized the withholding.

In other words, if Congress appropriates $X for the FBI to buy computers, then Congress didn't necessarily mean "the FBI shall spend exactly $X on computers, down to the cent". It could be interpreted to mean "the FBI may spend up to $X on computers". But Congress has clarified this ambiguity: https://en.wikipedia.org/wiki/Congressional_Budget_and_Impou...

> the Impoundment Control Act of 1974 specifies that the president may request that Congress rescind appropriated funds. If both the Senate and the House of Representatives have not approved a rescission proposal (by passing legislation) within forty-five days of continuous session, any funds being withheld must be made available for obligation.

In other words, if Congress appropriates $X for the FBI to buy computers, but the President thinks $X is excessive, then the President may ask Congress for permission to spend less than $X. If Congress doesn't grant the permission within 45 days, then the President must go ahead and spend the full $X. Again, Congress literally has the power to set the laws, and the President is required by his oath of office to execute those laws.

Furthermore, the Supreme Court already ruled on this exact question: https://en.wikipedia.org/wiki/Train_v._City_of_New_York

> President Richard Nixon was of the view that the administration was not obligated to disburse all funds allocated by Congress to states seeking federal monetary assistance under the Federal Water Pollution Control Act Amendments of 1972 and ordered the impoundment of substantial amounts of environmental protection funds for a program he vetoed, and which had been overridden by Congress.

That case seems directly analogous to what Musk is currently trying to do. Nixon lost that case in the Supreme Court.

Even if the Supreme Court did rule that the President had impoundment powers, it would probably be on the condition that "[the purpose of the law] could be accomplished by spending less than the appropriation’s total amount" (quoting from the page you linked). For example, the President would still be required to buy sufficient computers for the FBI, even if he spent less than $X on them. The President still wouldn't be able to just unilaterally decide "no, the FBI doesn't need computers, this is a waste of money".

So, I think it's already quite clear that Trump/Musk do not have the constitutional authority to just start cutting government programs. Do you agree? If not, which part do you want further clarity on?