As we have seen and known for a long time, Trump is the master of courtroom manipulation, delay and stalling.
But delay, stalling and manipulation are not the same as open defiance of a specific order. AFAIK, there are only 2-3 instances of the Trump administration openly defying a judges order, the most famous of which was the deportee flight to El Salvador that refused to turn around when a judged ordered them to mid-flight.
Otherwise, the Trump administration always appeals rulings, and if they are successful in getting a stay pending appeal, continue to act with lawless impunity. But if they dont get a stay, and the injunction remains in place pending the appeal, then they comply- most notably in the following instances :
No troops deployed to Chicago or Portland
Kilmer Garcia is free on US soil
Numerous Federal employees fired by DOGE had their jobs reinstated
These are the most well known, but there are numerous others, perhaps not captured accurately by your Google AI summary because they werent widely covered by the news media (not sexy enough), and so didnt get scraped by the AI bot compiling the summary, although the bot acknowledged this in your bolded portion of your post.
In that gray area between defiance and compliance with a judges order are the myriad legal games Trumps lawyers play in court, perhaps best exemplified by the cat and mouse contempt proceedings in Judge Boasbergs court. Boasberg has not found Trumps team in contempt yet, as they use procedural delays to stall their compliance with his orders.
Until/unless a stay is ordered pending appeal, it appears the administration is complying with the ruling reported in the OP, hence my post that he has already been stopped, at least for the moment.