Ravenfield with some mods on Workshop maybe? Or Operation Harshdoorstop with some Workshop.

Nothing more cozzy than shoot your friend in the head

Cyberpunk on easy with aim assist is pretty chill. Popping heads and blowing off limbs. It’s a comfort game for me.

Even though they're not traditional shooters, the Ratchet and Clank games are really fun. There's a pretty big genre difference in the games in the franchise, with generally the earlier games being more platform-ey, especially 1 & 2. A lot of the humor from the original trilogy still holds up today.

There's definitely some "unfun" parts in the games (giant mech fight from rac2 and the hacker from rac3 come to mind) but overall cozy imo. Some of the most unique and fun guns in any game.

If you're looking for strictly more shooter, check out Ratchet Deadlocked. There's barely any platforming and no mini games that I can remember, it's pretty much all shooting. NG+ makes it super cozy. It's really nice to play emulated.

Give GUN JAM a try. It's a rhythm shooting game, the stakes are as high or as low as you want them. There's only a minimal story and you just focus on the music, aiming and staying on the beat. Can be a lot of flow state fun.

payday 2 was kind of a cosy game where me and my friend would do heists whilst making tea and fetching snacks.

shadow raid? More like food raid 😊

Earth Defence Force: nothing better than blowing up 5 million bugs a minute after a tough working day

INCISION and ULTRAKILL

I felt the first Mass Effect was cozier than the sequels, though I never finished the sequels.

Smash Out has that aesthetic, although it can get infuriating. I also second the recommendation of Ravenfield.

What about Extraneum? It's cute as a button and very chill with plenty of things to shoot. It feels a bit like a modern wolfenstein since there aren't any stairs. Gunplay feels nice and the secrets are rewarding. Plus between levels there are funny data discs to read.

This might be a weird answer but I find Battlefield 1 very cozy.

Combat Master, a free to play CoD like.

I've been replaying Borderlands 3, so honestly I'd recommend any of those games for a cozy shooter. The stories don't take themselves too seriously, if you die you can just respawn immediately in the vicinity, and it can be pretty relaxing to just mow down waves of bandits or whatever other enemies.

Left4Dead 2

Great flow game

Maybe Destiny 2? The gunplay is unmatched and popping alien heads off in an explosion of alien blood or exploding robots in an explosion of robot blood is very satisfying.

Some parts are free to play too.

Bulletstorm. It's not about survival as much as killing enemies as creatively as possible. And the writing is brilliant in its stupidity. One of my favourite games of all times.

Hedon would be an option. It has actually calm moments, is cut scene free and gives you time to explore, whil still having cool combat moments.

It although has a pretty good difficulty mode.