I want to make an FPS controller that feels realistic, like when you move you really feel that your character has mass. In Unity I would've done that with RigidBody, but how do I do that in Godot 4.3.1 with CharacterBody3D? I know that RigidBody3D is not suitable for character controllers. May anyone show me the direction in which I shall dig?
Who told you rigid body isn't suitable for characters? If you're comfortable with the concepts of a physics engine and don't mind using impulses, force integrators and other physics-driven locomotion, I see no reason to avoid a RB character.
For most use cases, rigidbody just a bigger challenge to get simple things "working right", and the precise control a kinematic body provides tends to be favorable.