The Youtube channel Legal AF has a breakdown of the legal process up to now.
What's a bit interesting is that while the Supreme court hasn't done much to bring Gracia home, they also did send the case back down to the lower courts.
It's that lower court judge who immediately damned Trump bring Garcia home and give daily updates on their progress.
Trump seems to be in-contempt of those orders leaving many questioning how the judge will react to today's filing.