You can't kill non-targets, be caught doing anything illegal, or let any bodies get discovered (unless it was an accident kill), but you absolutely can use guns. You can use them on the target, shoot out cameras, use them for distraction or panic shots, blast open locked doors, drop them on the ground to pull an NPC off their route, etc.

The game is a sandbox. They give you a ton of tools and it's up to you to figure out how to use them. You're meant to play each level over and over in a variety of ways (as shown by all the mastery challenges) and having all these different tools at your disposal is part of what makes that fun. But if what's fun for you is to mow everyone down with a shotgun, then go for it. There's no in-game incentive to try for silent assassin on every run.

I really enjoy watching Hitman competitions on YouTube. You'll have like one person blowing up propane tanks, one person sniping the targets from across the map, and one person using poison and tasers, with all of them finishing with the top ranking and within seconds of each other. It's wild to me how many viable ways the game gives you to kill targets and how creative it allows you to be.