A lot of semi auto handguns won't fire if you press the muzzle too hard into the target. The Beretta design as well as the Taurus 92/99's for example. When the barrel pushes back it disengages the trigger.
I'll make a wildly inclusive statement and say that ALL pistols using a locked breech design sim to the 1911 design will not fire if the barrel is pressed against the target hard enough to move the barrel back. I imagine exceptions exist but offhand, I can't think of one. Fixed barrel designs don't have that "problem" if indeed it is a problem. Now, as to the fun gun battery category, I can't think of a 3 gun battery that would not qualify as fun, some more than others. For sure there's a 22 or 2 in the mix.
Good advise on the Beretta 21a .I might add that Being a short barrel it is important to be using the highest velocity ammo available ,if for self defense. CCI mini mag come to mind . Then there are guns like this sold as what dad called belly busters, sold in 1886-1896. Still a functional weapon I only shoot .22 shorts and snake shot, though it will accept long rifle, but I'd never push it that hard . These go as far back as the .22 round it's self.
The 21A can be very ammo sensitive.The one I have was used to teach all 4 of my children to pistol shoot. Being able to go from single shot to a semi auto after they were comfortable with it was the main reason for my purchase. I've never desired to have one in any other calibre. It is a finely made pistol over all but it does need to be kept clean. Nowadays it's seldom used other than to put down a wounded or dying animal. Loaded with CCI Stingers it works well for this with minimal mess or noise. As a belly gun I carry a NAA .22 mag 5 shot revolver. Less to go wrong with a revolver, it's SS so it wears very well for a daily carry in my front pocket.