Branch and don't have the authority to issue orders and injunctions when the EB is following its legal authority. Only the Supreme Court is co-equal.
If The Supreme Court Is Going To Ignore The Constitution, Trump Should Ignore The Supreme Court
https://thefederalist.com/2025/03/06/if-the-supreme-court-is-going-to-ignore-the-constitution-trump-should-ignore-the-supreme-court/