How do we access and write content to the group container? Also, apart from the SafariWebExtensionHandler's beginRequest(with:) function, is there some other native call back we can get?
Safari Web Extension writing content to the group container
You can use the WebExtension native messaging API to communicate between your extension's JavaScript and your app extension's native code.
Check out https://developer.apple.com/documentation/safariservices/safari_web_extensions/messaging_between_the_app_and_javascript_in_a_safari_web_extension?language=objc