Inside of func _physics_process(delta) you have the following section:

    var input_dir = Vector2.ZERO
    if mouse_captured:
        input_dir = Input.get_vector("ui_left","ui_right","ui_up","ui_down")
    var cam_basis = Basis(Vector3.UP, yaw)
    var direction = (cam_basis * Vector3(input_dir.x, 0, input_dir.y)).normalized()
    if direction != Vector3.ZERO:
        velocity.x = direction.x * SPEED
        velocity.z = direction.z * SPEED
    else:
        velocity.x = move_toward(velocity.x, 0, SPEED)
        velocity.z = move_toward(velocity.z, 0, SPEED)

I believe this means that you are requiring direction to be equal to Vector3(0,0,0) in order for the velocity of the CharacterBody3D to move towards 0 (i.e. stop). This is likely the cause of the character continuously moving as the input is likely to equal 0 often during regular mouse movement.

Could you describe the character and intended control/movement? Why was this initially implemented to always move the character?

Happy to try and help with more context!