There is the new Doom as already mentioned. Wolfenstein The New Order might also fit the bill as it does integrate some older and more over the top FPS elements. Serious Sam 3 is another good one if you just want to fight your way through hundreds of enemies with a huge arsenal of weapons (I recommend playing the game in Serious Sam Fusion though, the original release has some CPU bottlenecking issues in some of the larger fights that the Fusion release fixes with Vulkan support).
Shadow Warrior (2013) might also be up your alley, though that game does have a bit more focus on melee with the sword being a major weapon throughout the campaign. Shadow Warrior 2 has similar shooting mechanics to the first, but is more of a looter shooter in a similar vein to the Borderlands series and there is an emphasis on stats and weapon upgrades that isn't present in the first game.
Finally if you just want an old school FPS with more modern graphics and literally nothing else changed about it, you might want to check out the 2013 Rise of the Triad game.