I was through JFK T1 a month ago, and the Air train was back to running both ways. They still had signs about the transfer and buses, but it worked well enough to take the LIRR in, AirTrain from Jamaica to T1, go to the AF desk, take the train to T5 to see the influencers playing dress-up in the lobby of the TWA hotel, and take the train back the other way.
Of course, JFK is always a pain to get to. The buses made things worse.