Meh I love FPS games and here is how I would categorize things.
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movement shooters (subcategories singleplayer and multiplayer) -> Xonotic, Quake, Unreal Tournament, Ultrakill, Doom etc...
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battlefield awareness/combined arms games -> Battlefield, Battlefront, Insurgency, Easy Red 2, Angels Fall First, Operation Harsh Doorstop, Project Reality etc... I also include battle royale style shooters here as they also primarily test battlefield awareness.
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repetitive aim focused games on small memorizable maps -> Call Of Duty, Counter Strike, Valorant etc...
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pve swarm focused games -> Deep Rock Galactic, LFD2, Hell Divers, Warhammer Darktide