How to move a DisplayObject left/right taking into account its direction?

[badatmath]

Here is most of the code to get the point across...

// init time

const direction = new Vector2();
const speed = 5;

// render time

direction.x = mouseX - window.innerWidth / 2;
direction.y = mouseY - window.innerHeight / 2;
direction.normalize();

const deltaY = direction.y;
const deltaX = direction.x;
const angle = Math.atan2(deltaY, deltaX);

player.rotation = angle + 90 * Math.PI / 180;

if (forward) {
  player.position.x += direction.x * speed;
  player.position.y += direction.y * speed;
}

if (backward) {
  player.position.x -= direction.x * speed;
  player.position.y -= direction.y * speed;
}

if (left) {
  // how?
}

if (right) {
  // how?
}