Not a separation of powers issue. The administration fied a legal brief, arguing for a certain position ( that the execution should be halted). The administration’s position is, as usual, dead wrong, but the fact that they filed a brief is not a separation of powers issue.
I’m of the opinion that real legal issue is compliance with the treaty.
Does the treaty REQUIRE the defendant to be notified that he has the right to contact the consulate? If not, then there is no reason to stop the execution
Even if there is the requirement - Was he notified by anyone prior to his trial that he has the right to contact the consulate? Including his defense team?
Did someone else, acting on his behalf, contact the consulate? Perhaps a relative?
If he did contact the consulate, or if someone contacted the consulate on his behalf, there is no reason to stop the execution
Was he afforded the opportunity to contact the consulate and then refused? This would require a proof positive in that it is a bit of a negative. In other words, there would need to be a document that showed he chose not to contact the consulate.
The post to which I replied asked how he could “tell SCOTUS what to do”, and if he were trying to do that, separation would apply.