Well, that said there is (SILI), which is statin-induced lung injury. It's not common though, and I am not sure but I think it comes with other symptoms like a cough and fever, so if you are getting that combination then I would press further medical tests. Some meds can also cause respitarory depression, especially some CNS depressants. I always check sites like: https://bnf.nice.org.uk/interaction/ whenever offered a medication because although one medication on its own may not have the adverse effect, it may in combination with another. I've had a few GPs not check this and I've pulled them up on it and made them switch medication.
Nothing in this post stroke life seems certain but we have to deduce shrewdly in order to eliminate worry and fears.
However, on a purely stroke basis, reduced respitarory drive and cerebellar stroke is common. I have it and I am pretty sure it has no relation to the statins I am taking. You can ask for a respitarory assessment through your GP as a referral. It is done at the hospital.
So, back to the stroke symptom, the only thing that has worked for me is breathing exercises and learning breathing control. Because we can take back control of it, it just takes practice.
There are lots of resources online, this one is from the NHS (https://www.uhb.nhs.uk/Downloads/pdf/PiBreathingExercises.pdf).
At the end of the day, it is fixable. If it is not a serious underlying condition, we can still breath, and that is the main thing. We just need the cerebrum to take over some of that responsibility.
Anxiety magnifies everything, and also if you are focussing too much on it, it can make breathing more laboured because you think you need more oxygen, so the cerebellum kicks in and tries to take in emergency air and because of the misfiring of communication it becomes very laboured and you feel breathless - Catch-22. Remember, that even if you think you aren't thinking about something, even just a quick thought will get the cogs ruminating in the background. Like with panic attacks, they have worked out that panics aren't instant, sometimes the seed is planted hours beforehand or even days.
I noticed my change at about the third month in, I needed to take a deep breath when turning in bed. Since then, it has become pretty regular and uncomfortable but not distressing. I did a fair amount of research into it because like you I was alarmed. However, at the same time, I had trouble swallowing saliva. So, I practiced for a month or two, swallowing, and also swallowing with a small amount of liquid. Nowadays, I can swallow fine. I think I retrained my brain to swallow because that too was fairly uncomfortable.