I love the fact that the announcement couches the order in the state's prerogative to consume services that it deems best fit its needs, which is very slick politically, however that works legally.
I think that the state can do that, yes. It can't say "you have to do this to do business in our state", but it can say "you have to do this to do business with us, the state government".
The alternative is that the federal government can dictate which businesses the state governments do business with, which is, to put it mildly, probably not a valid use of federal power.
The alternative is that the federal government can dictate which businesses the state governments do business with, which is, to put it mildly, probably not a valid use of federal power.