Happened to us, LHR to JFK two weeks ago, got the text message but no other announcement. Waited for our luggage with around a third of the plane but finally announced there was no more luggage loaded. We were lucky in that we were stood next to ground staff that took us to the office to report, we were there completing forms for about 20 mins whilst a massive queue had built up behind us. Luggage was couriered to the hotel the next day.
This was the start of a short break from hell. No heavy duty rain coats as had 'thoughtfully' packed them in the front of the case, we got very wet finding the hotel, plus no dry clothes to change into, Two days later we both came down with a bad dose of Covid and spent a lot of the break in bed. Finally due to the torrential rain, we had to make a dash to the airport on the final day when the Governor of New York issued a state of emergency and said not to travel. Got to spend 4 hours in the lounge (the bar) and by the time we were on our way home slept through the whole journey missing my first club suite experience.