I know this has a ways to go to play out, but I’d be shocked and disappointed if this passed constitutional muster simply because we have a case where (i) congress (who has the sole authority under the constitution to appropriate funds) discussed appropriating funds to basically the exact same things, and (ii) actually DID appropriate some funds to that thing.
If the president can redo the budget to get closer to what he wants by declaring an emergency (which there is apparently no standard for), then he has the same budgetary powers as congress. If that’s the correct application of the statutes then those laws just have to be unconstitutional.