Sword pistols are a weird historical oddity. They exist, mostly from the 18th century (not counting the modern gunswords specifically patterned off Final Fantasy.)
The problem is, they don’t really work that well. The extra weight makes the pistol harder to aim, while the modifications to include a functional gun reduces the sword’s balance, increases the weight, and undermines it’s effectiveness.
I’m not sure about a gun/axe combo, but to an extent you’re looking at the same basic concessions.
The one good counter example are bayonets. At a really reductive level, you could call those a combo weapon. Though in that case, you’re talking about using a longarm, and a lightweight melee weapon. My understanding is that the extra weight of the blade does make the weapon a little harder to operate, but, the entire idea is you’d be attaching the bayonet when you weren’t expecting the gun to be enough on it’s own anyway.
There may be some integrated longarm with an attached blade that I’m unaware of, so the gun axe or a gun halberd is just this side of plausible. But, again, I’ve never heard of any historical examples.
Combo weapons can also include things like an under-slung grenade launcher, shotgun, or other attachment. For what they’re intended to do, those work. Though it’s probably not what you were thinking of.
There’s also the Lemat pistol. This was a .36 or .42 caliber revolver with an integrated 20 gauge shotgun in the center of the cylinder, and designed to fire from a secondary barrel located under the primary. Again, it’s more of a historical oddity than a practical weapon, as less than three thousand of these pistols were originally produced. Though I believe you can buy modern reproductions chambered in .44, 20 gauge.