I was surprised to learn apparently these axe-guns were actually really popular, especially in Poland. I honestly thought it was a gimmicky joke when I drew the picture, the equivalent of Mall Ninja gear for that century, but apparently axe guns were just a thing that people did and there were lots of them. Here's a picture of a Polish museum piece for comparison, yoinked from Wikipedia.
I guess tactically I can see this for cavalry, opening up a bunch of holes right before your charge hits would make a cavalry attack much rougher, and you may not have a chance to swap weapons. That still seems really niche though and I'd think you'd want a proper cavalry weapon, perhaps not a gunlance since lances broke so easily but maybe a Gunsaber? Why an axe? Did cavalry frequently do attacks with an axe?