How is a new address form popup implemented on the frontend checkout screen in the shipping section?

The «+ New Address» button:

Click handler:

It switches visibility of the address form through the data-bind:

Address form popup

The address fields are rendered into the additional-fieldsets display area:

The first part of the fields configuration (it has a priority over the second part)

The second part of the fields configuration

\Magento\Customer\Model\AttributeMetadataDataProvider

The provider loads the customer address attributes (the attributes of the customer_address entity type) from the Magento 2 database.

See also: