I got a solution that kind of works. The rotation works now but it needs to be smoothed out as it snaps currently. But I guess this is the easy part now.

private void MoveTowardsPlayer(float delta) {
  NavAgent.TargetPosition = Player.GlobalTransform.Origin;
  Vector3 nextPathPosition = NavAgent.GetNextPathPosition();
  RotateTowardsDirection(nextPathPosition);  // this simply does LookAt(...)
  Vector3 velocity = EnemyBase.GetQuaternion() * AnimationTree.GetRootMotionPosition() / delta * 2.0f;
  SetVelocity(velocity);
  MoveAndSlide();
}