At one time, I have found a YouTube video describing how to fix the noise cancelling issue by literally sucking on the external microphone grille of the malfunctioning AirPod. Oddly enough, it did fix the problem temporarily. I think there may be a valve that is used to equalize the pressure between the sealed ear and the outside, and if that gets stuck opened or closed the noise cancelling fails. In my case, low frequency sounds were passing through. Very annoying.
Worth noting, I had the clicking noise issue with Sony WH-1000XM3, too. The behavior was exactly the same as with the AirPods Pro. Whenever a change in pressure occurred (door/window closed or opened), and during walks or even just moving the head in certain ways, the clicking noise started. This only happened when ANC was active, both for AirPods Pro and for the Sonys.
With Apple, I never had any problems getting a replacement, and it was in two countries that do not have official Apple Stores. However, with the Sony it was a completely different story. I had them fixed in warranty, just to find out they were not actually fixed. They replaced the headband that had really nothing to do with the problem. Eventually, after lots of emails and calls, the store I bought them from just gave me back my money.