Magento 2 : Event Observer For Shipping Address Selection

You should use plugin to get the shipping info:

Your di should be under etc folder: app/code/Extension/Vendor/etc/di.xml

<?xml version="1.0"?>
<config xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:framework:ObjectManager/etc/config.xsd">
    <type name="Magento\Checkout\Model\ShippingInformationManagement">
        <plugin name="get_shipping_info" type="Vendor\Module\Plugin\Checkout\Model\ShippingInformationManagement" sortOrder="1"/>
    </type>
</config>

Your Plugin:

/**
     * @param \Magento\Checkout\Model\ShippingInformationManagement $subject
     * @param $cartId
     * @param \Magento\Checkout\Api\Data\ShippingInformationInterface $addressInformation
     */
    public function beforeSaveAddressInformation(
        \Magento\Checkout\Model\ShippingInformationManagement $subject,
        $cartId,
        \Magento\Checkout\Api\Data\ShippingInformationInterface $addressInformation
    )
    {
       ......
    }

    public function afterSaveAddressInformation(
        \Magento\Checkout\Model\ShippingInformationManagement $shipping,
         $result
    )
    {
        ......
    }