You should really give the Wolfenstein games a try if you already own them. After about an hour or two you will know if the game is for you. Start with New Order.
There is no melee weapon in Prey, except the wrench you start with. It is a Sci-Fi game, set on a space station. The focus is on finding your own solutions to problems by using different skills you unlock. Strength, hacking, stealth and so on. It is an immersive sim, but you can play it like a shooter too. It demands some attention though, or you will not know what to do next.
Turbo Overkill has multiple levels you complete one after another. It is a classic FPS game with a campaign. The big fights happen in large arenas though. The game is very fast and you have to use a lot of different movement abilities to survive on harder difficulties.