Define the extension attribute in XML

app/code/Vendor/Module/etc/extension_attributes.xml

<?xml version="1.0"?>
<config xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:framework:Api/etc/extension_attributes.xsd">
    <extension_attributes for="MagentoCheckoutApiDataShippingInformationInterface">
        <attribute code="address_two" type="string"/>
    </extension_attributes>
</config>

Assigning the value for extension attributes in knockout js 

app/code/Vendor/Module/view/frontend/web/js/shipping-save-processor-default.js

saveShippingInformation: function () {
                var payload;

                payload = {
                    addressInformation: {
                        shipping_address: quote.shippingAddress(),
                        billing_address: quote.billingAddress(),
                        shipping_method_code: quote.shippingMethod().method_code,
                        shipping_carrier_code: quote.shippingMethod().carrier_code,
                        extension_attributes: {
                            address_two: $('form.form-shipping-address input[name="address2"]').val()
                        }
                    }
                };

                return storage.post(
                    resourceUrlManager.getUrlForSetShippingInformation(quote),
                    JSON.stringify(payload)
                ).done(
                    function (response) {
                        quote.setTotals(response.totals);
                        paymentService.setPaymentMethods(methodConverter(response.payment_methods));
                    }
                ).fail(
                    function (response) {
                        errorProcessor.process(response);
                    }
                );
            }

Save Extension Attribute to quote table using beforeSaveAddressInformation method using Plugin

app/code/Vendor/Module/Model/Checkout/ShippingInformationManagementPlugin.php

namespace VendorModuleModelCheckout;
/**
 * Class ShippingInformationManagementPlugin
 * @package OyeDeliverydateModelCheckout
 */
class ShippingInformationManagementPlugin
{

    protected $quoteRepository;

    /**
     * @param MagentoQuoteModelQuoteRepository $quoteRepository
     */
    public function __construct(
        MagentoQuoteModelQuoteRepository $quoteRepository
    ) {
        $this->quoteRepository = $quoteRepository;
    }

    /**
     * @param MagentoCheckoutModelShippingInformationManagement $subject
     * @param $cartId
     * @param MagentoCheckoutApiDataShippingInformationInterface $addressInformation
     */
    public function beforeSaveAddressInformation(
        MagentoCheckoutModelShippingInformationManagement $subject,
        $cartId,
        MagentoCheckoutApiDataShippingInformationInterface $addressInformation
    ) {
        $extAttributes = $addressInformation->getExtensionAttributes();
        $address2=$extAttributes->getAddressTwo();

        $quote = $this->quoteRepository->getActive($cartId);
        
        $quote->setShippingAddressTwo($shippngaddress2);    
        $this->quoteRepository->save($quote);;

    }
}

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