First things first, download Tactical Battlefield - it's a popular mod based around PvP gameplay.

When people call Arma a walking simulator, they're only half-joking - in truth I think what makes Arma so appealing is just how punctuated the action is by long stretches of what amounts to really nothing - spending 20 minutes just travelling to your destination and then being killed from a kilometer away in an instant is a real possibility and it can get annoying fast, but it's also part of what makes Arma what it is at its core.

So I see why missions that attempt to ramp up the intensity exist and why many people gravitate towards them, but as you've outlined they have their own shortcomings. New players often scoff at the idea of cooperative gameplay against the AI which itself has without question a ton of issues, but player-versus-player combat is effectively neutered when the overwhelming majority of the servers running those modes exclusively simultaneously allow third-person, which removes any semblance of tension that makes an encounter compelling.

The thing to appreciate about Arma is that it isn't at all like any other modern FPS - sure you can make a mission to emulate the pace of Battlefield of Call of Duty but that's just putting lipstick on a pig. While other games try to overload your with stimulation constantly, Arma offers it in brief and exaggerated spurts, and it's because both exist and are different that they are great.

I really recommend playing a match of either EUTW or BECTI, both found using the Type filter 'Capture The Island' - these blend cooperative and player-versus-player gameplay across the whole island.