Aren't the National Guard already funded by the government, either state or federal? In which case you are probably quite right. The "donation" has more than likely gone into the governor's pocket, not a government treasury.
it's complex. The National Guard is surpervised by the US Army, but controlled by the individual states. (THe US Army Reserves is completly different)
The usual head of the Guard is the Governor of the state.
It's a part time service, only a small permanent staff are full time in the Guard.
The Guardsmen usually get only a fraction every month of what a Full Time soldier in the regular army would get which is paid for by the states.
But when he is called to full time duty..the term is activated..he gets the same full time pay as someone of his rank would get in the regular army as long as he is activated.
What this means is when the Guard is activated, the cost goes up a lot.
The US Government can call National Guardsmen..either as a unit or as indivduals to service into federal service, making them part of the regular army on a temporary basis, but when this happens the Feds pick up the tab.
The National Guardsmen on duty in DC after the Jan 6th Insurrection, were sent by nearby states but were paid by the Feds.
And it';s not unusual for one state's guard to deploy to another state during a natural disaster to help out..but the sate they went to have to pick up the tab unless federal disaster relief does.
Apparently in South Dakota, if the Guard is deployed outside of the state, the Feds or the state they are deployed to have to pick up the extra expense. The feds are not picking up the tab for the SD deployment, and neither is Texas apperently. So Noem went to a private individual to pay for her little political stunk.
What Noem is doing stinks on ice, frankly.
Which is why I keep making the reference to the Hessians, who were soldiers from several different German principlaties who were basciallly rented out by their princes to the British government during the American Revolution to help put down the rebellion. Not all were from Hesse, but the term "Hessian" stuck. It is NOT a favorable term when used by an American.
Hope that helps. Our Federal system, where the individual states have greater powers and more indepdence then the stated or provinces in most countries is something a great many used to a more centralised government have problems grokking.