That was a different situation because those people continue to be employees. The gov gave them back pay during shutdown because it wants them to continue to work after the shutdown (so services keep being rendered).
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).
I recall there being some significant gaps, so these people had already returned to work.
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 transportershttps://en.wikipedia.org/wiki/Radiation_Exposure_Compensatio...
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).