Godot 4 move relative to rotation

xyz

You need to rotate the velocity vector passed to move_and_slide()

xyz

It'd be easier to help you if you post some actual code.
Using one of the basis axes of body's global_transform as the velocity direction should do the trick.

xyz

You could approach it like this, assuming z axis is the forward axis:

var forwardSpeed = 2.0
var rotationSpeed = .1

func _physics_process(delta):
	rotate_y(Input.get_joy_axis(0, JOY_AXIS_LEFT_X) * rotationSpeed)
	velocity = global_transform.basis.z * forwardSpeed
	move_and_slide()