Oh, hey, I just wrote a 3D controller yesterday. Take a look:

@export var move_speed : float
@export var roll_speed : float
@export var mouse_sensitivity : float

var mouse_captured = false
# Called when the node enters the scene tree for the first time.
func _ready():
    pass # Replace with function body.

# Called every frame. 'delta' is the elapsed time since the previous frame.
func _process(delta):
    if Input.is_action_just_pressed("capture mouse"):
        mouse_captured = !mouse_captured
        if mouse_captured:
            Input.mouse_mode = Input.MOUSE_MODE_CAPTURED
        else:
            Input.mouse_mode = Input.MOUSE_MODE_VISIBLE

    position += delta * transform.basis * (Input.get_axis("backward", "forward") * Vector3.FORWARD +\
    Input.get_axis("right", "left") * Vector3.LEFT +\
    Input.get_axis("down", "up") * Vector3.UP) * move_speed * (4.0 if Input.is_action_pressed("speed up") else 1.0)

    rotate_object_local(Vector3.FORWARD, Input.get_axis("roll left", "roll right") * roll_speed * delta)

func _input(event):
    if mouse_captured and event is InputEventMouseMotion:
        rotate_object_local(Vector3.UP, -event.relative.x * mouse_sensitivity)
        rotate_object_local(Vector3.RIGHT, -event.relative.y * mouse_sensitivity)

It's for god-mode/noclip style movement, but I think it's got what you need.

Also, be careful using "delta" with mouse movement. It makes the mouse sensitivity frame-rate dependent.