Yeah and we need to remember that there are two: one in NY Superior Court by Engoron forbidding statements about court staff, but not about Engoron or others. Trump has now been tagged on that one twice. It has not been stayed and any appeal status is unclear. It's probably so narrow as to be pretty unassailable.
The other is Chutkan's in DC, which is broader. Under the Federal Rules, you have to first ask the trial court to stay an order in the nature of an injunction (which is what a gag order is), before you can ask the court of appeals to stay it. It's a bit bizarre, because why would a trial court stay an order it just saw fit to grant, but there it is.
Nevertheless, Chutkan did stay her gag order while they briefed the issue of the stay and, as soon as briefing was complete, or maybe before Trumpco replied (usual order of briefing is motion, followed by response, followed by reply, but replies are usually optional and may not be considered), Chutkan lifted the stay and denied the motion for a more formal stay.
Now it's teed up for the DC Circuit for a stay pending appeal.