Always be moving/dodging, do glory kills for health, chainsaw for ammo, and most importantly master the Quick Switch technique. This person has a great guide on it. It's basically where you switch weapons after every shot so you don't have to reload and you output damage really fast even on the hardest difficulty.
Given that you are on a controller you can just swap between 3 weapons and still delete enemies. Like here is my play through with my steam controller where I pretty much spammed super shotgun, ballista, and rocket launcher to get through the game on nightmare. There was an update pushed that lets controller uses bind weapons to any button, so set weapons to quick switch with that over relying on the weapon wheel which breaks momentum.
I've used the Steam Controllers for many years and use dual touchpads for movement and camera. Here's me playing Doom Eternal, Anger Foot, and a video on why I prefer touchpads to joysticks.
But, despite that I'm not a big of a fan of the ones on the Steam Deck. The placement is not that comfortable. There are 3D printed grips though that I would like to try out that would let me hold the Deck so it is more like holding the Steam Controller with the touchpads. Until then a majority of my gameplay is done with the joysticks in contrast to on the desktop where it is with touchpads.
I am really glad the touchpads are present so that it's not an input Valve has abandoned, but the placement and ergonomics is really disappointing me. I'd be playing lot of FPS games on the Deck if the touchpad experience were more on par with the Steam Controller.