I’ve done some looking on this in the past as well and my take was that milk/dairy doesn’t increase mucus production, but the fat and proteins in dairy can increase mucus adhesion. So while you don’t increase production, what you do typically produce can become more sticky and harder for the body to clear (particularly in the mouth/throat/esophagus where physical contact occurs). Been a while since I looked into it, but definitely recall that the science shows higher mucus production caused by dairy is a myth. Just be careful not to confuse lack of higher mucus production with lack of negative effects dairy may cause.
edit: actually think it was sticky mucus back when I was in a sound booth that an audio engineer recommended sipping some apple juice to clear my throat. Definitely worked for me, and science backs it. Think they make throat lozenges with pectin now as well. Not for asthma – just for loosening mucus present in the esophageal tract.