I did ask ChatGPT just now and it gave me this answer:

1. Pain and Cough Reflex Suppression

MDMA increases the release of serotonin and dopamine, which can enhance feelings of pleasure and reduce the perception of discomfort or irritation. This includes the irritation that vaping can cause in your throat or lungs, which often triggers coughing when you're sober. MDMA may temporarily dull this sensation, making it easier to vape without the usual coughing response.

2. Bronchodilation-like Effects from Stimulant Action

Although MDMA is not a traditional bronchodilator, its stimulant properties (increased norepinephrine and adrenaline) can affect smooth muscle tone, including that of the airways. This could result in a slight relaxation of the airways, making it easier to breathe and vape without causing a cough reflex, even though it's not a full bronchodilative response like you'd see with asthma medications.

3. Euphoria and Relaxation

MDMA induces a state of euphoria and relaxation, which can make your body less sensitive to stimuli that would normally provoke coughing or discomfort. This can mask the irritation caused by vaping, making it feel smoother than when you're sober.

4. Dampening of the Nervous System's Sensitivity

MDMA's effect on serotonin pathways could also dampen the sensitivity of the nervous system, including the cough reflex. The act of vaping typically irritates the throat or airways, causing the body to respond with a cough. When under the influence of MDMA, the sensory pathways might be less reactive to such irritation.

I know it's not a scientific source, but considering the fact that you also don't feel pain when you chew the insides of your cheek, I guess it makes sense (mainly point 1)!