They exist, but are more niche. See, for example, the Savage takedown rifle that shoots 22lr / 410 shotgun shells. https://www.savagearms.com/content?p=firearms&a=product_summary&s=22440

Clearly it's geared towards more of a survivalist/bug-out type scenario, where you might need the 22lr for a squirrel and a 410 for game more substantial.

Obviously several revolver calibers are multi-use too - 357 mag revolvers can all shoot 38 special ammo, for example. Shotguns are also very versatile, letting you shoot slugs/buckshot/birdshot/whatever, all out of the same tube.

I think the increase in ballistic technology has basically made multi-caliber guns fairly obsolete, but I'm no expert. But if you're carrying something pistol-sized like the article shows, I would imagine you would benefit mostly from just more magazines of 9mm, rather than trying to make a clunky shotgun attachment for a pistol, leading to (1) more complexity in the pistol, meaning more possibilities of something going wrong, (2) need to carry multiple calibers, and (3) more difficulty in training to use both calibers effectively out of the same pistol (i.e. hold it like this for 22lr, hold it like this for 44 magnum).