The code for a first person movement youtube tutorial in Godot 4

Godot4FPS.gd

extends CharacterBody3D


const SPEED = 5.0
const JUMP_VELOCITY = 4.5

# Get the gravity from the project settings to be synced with RigidDynamicBody nodes.
var gravity: float = ProjectSettings.get_setting("physics/3d/default_gravity")
@onready var neck := $Neck
@onready var camera := $Neck/Camera3d

func _unhandled_input(event: InputEvent) -> void:
	if event is InputEventMouseButton:
		Input.set_mouse_mode(Input.MOUSE_MODE_CAPTURED)
	elif event.is_action_pressed("ui_cancel"):
		Input.set_mouse_mode(Input.MOUSE_MODE_VISIBLE)
	if Input.get_mouse_mode() == Input.MOUSE_MODE_CAPTURED:
		if event is InputEventMouseMotion:
			neck.rotate_y(-event.relative.x * 0.01)
			camera.rotate_x(-event.relative.y * 0.01)
			camera.rotation.x = clamp(camera.rotation.x, deg_to_rad(-30), deg_to_rad(60))


func _physics_process(delta: float) -> void:
	# Add the gravity.
	if not is_on_floor():
		velocity.y -= gravity * delta

	# Handle Jump.
	if Input.is_action_just_pressed("ui_accept") and is_on_floor():
		velocity.y = JUMP_VELOCITY

	# Get the input direction and handle the movement/deceleration.
	# As good practice, you should replace UI actions with custom gameplay actions.
	var input_dir := Input.get_vector("left", "right", "forward", "back")
	var direction = (neck.transform.basis * Vector3(input_dir.x, 0, input_dir.y)).normalized()
	if direction:
		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)

	move_and_slide()

There is a bug - if you rotate the player node in the editor then the direction is not correctly mapped to the new orientation.

I don't know a good way to fix this, so I use this method:

var direction = ((neck as Node3D).transform.basis.rotated(Vector3.UP, rotation.y) * Vector3(input_dir.x, 0, input_dir.y)).normalized()

thanks so much