The Supreme Court denial is just words. He stopped implementing the previous plan because he accepted and followed those words, but he could not. Maybe his bureaucracy will reject him and refuse to go against the Supreme Court words, but that’s a question for his bureaucracy.
And yes, that’s how coups work. Sometimes the army/police/whatever backs down because some other entity in the civil power structure says “you can’t do that”. And other times, they don’t. It’s all decided based on the perceived power and righteousness of the two sides, not because the court just decides stuff and then it happens by some sort of magic.
Speaker of the House is the guy that gets to choose a lot of things on the capitol grounds. And new congressmembers are sworn in on January 3rd, so we’re already in the new Congress.