They had it on an expedited basis, with Trump's brief due in September. Trump moved to extend that a month, and Smith did not oppose.
Appellee's brief due October 25, 2025. Government's reply due 21 days later. https://www.courtlistener.com/docket/68955302/united-states-v-donald-trump/
I'd imagine they have oral argument in December and a ruling by January. Educated guesses only.
EDIT TO ADD: I said it was expedited because the appeal was noticed on July 8, and the briefing schedule putting the government's brief due August 27 is pretty fucking swift. HOWEVER, the briefing dates stem from ordering and receiving the record from the trial court, as you probably know. On July 24, the government certified that all documents were on file.
Because this is an appeal of a discrete order, I guess there isn't much record on appeal and the transcript of the hearing is mostly irrelevant because it was non-evidentiary. So maybe just going fairly fast on that alone.