This can be simplified to:
/**
* Map STEP_SELECT_ADDRESSES to Cart::CHECKOUT_STATE_BEGIN
* @return void
*/
public function beforeSave()
{
if ($this->checkoutSession->getCheckoutState() === State::STEP_SELECT_ADDRESSES) {
$this->checkoutSession->setCheckoutState(\Magento\Checkout\Model\Session::CHECKOUT_STATE_BEGIN);
}
}