I hesitate to call Doom and Apex movement fluid. Well, it is fluid in the sense that it feels like you're on cart with exquisitely greased bearings and futuristic servos. FPS movement is inherently unnatural because no organism moves like that. That's not to say they don't control well, but they don't control naturally. Third person games can actually flow naturally, because you can animate things like turning around, changing direction, momentum, etc.
FPS characters have invisible crab legs.