So future administrations are likely to retroactively approve payments if it becomes a political issue. Honestly taking the buyout without an act of congress backing it is likely the more risky here unless you where already planning to leave which is likely why most people took it.
You need to replace lower level employees as Trump is trying, and at 1% adoption mostly failing to do.
In this case, Trump/Musk don't want these workers back, so there's no political incentive or pressure to pay them. They can just not do so if it's "not funded by Congress" (usually there's fine print about this, at least there is in gov contracts, which are similar).
But it’s not just about current workers, new administrations have handed out money to people for past issues years or sometimes decades after the fact. Just as an example the 1990 Radiation Exposure Compensation Act was about compensation for people exposed during the Cold War.
$50,000 to individuals residing or working "downwind" of the Nevada Test Site $75,000 for workers participating in atmospheric nuclear weapons tests $100,000 for uranium miners, millers, and ore transporters https://en.wikipedia.org/wiki/Radiation_Exposure_Compensatio...