how can retailers integrate their app's built in search functionality with Siri using the system domain

Retailers can integrate their app's built-in search functionality with Siri using the system domain by following these steps:

Define an App Intent: Create an app intent that leverages your app's existing search functionality. For example, if your app has a method to display search results, you can create an app intent that uses this method.
Use the New Assistant Schema: Add a new assistant schema for search to your app intent. This allows Siri to route users directly to your app's search results UI. You can do this by adding a Swift macro before your app intent declaration.
Test with Shortcuts: Build and run your app to test the integration with Siri using the Shortcuts app. Create a new action in Shortcuts that uses your app's search functionality and test it to ensure it works as expected.

For a detailed demonstration, you can refer to the session Bring your app to Siri (13:35).