It seems like this could be explained by something as banal as sinus congestion causing/worsening COPD. And the link between gut health and general sinus congestion seems natural to me.

Articles like this tend to paint gut health effects in some kind of supernatural light.

My dad had COPD later in life, and I can attest that he was not a person willing to eat much fiber; I could easily believe his gut microbiome was screwed up.