As far as I know there is no setting. I miss a lot of stair climbs (as I also did w/ my F3 in the past). Probably over half of them. I find that if I lift my wrist to chest height or higher when reaching the next level it consistently records it but hit or miss when I don't. So I'm guessing that the altimeter is not seeing difference in altitude it expects for one flight of stairs. Would be good if there was a sensitivity setting for this...
My Vivoactive HR is terrible about missing flights of stairs, especially when I take 2 steps at a time. Meanwhile my iPhone catches the number of flights of stairs perfectly. I suspect Garmin's algorithm for stairs figures if I'm moving that fast, and covering that much altitude under a certain number of steps, I'm probably in an elevator.