I have a Google Smart Home action deployed already, and I noticed that when I open the Google Home app, there are some suggestions of apps to link to my Google Home (as shown in the image below), and those integrations are from apps that I have installed on phone, and as I add new apps that have integration with Google Home, the app start to suggest to integrate with Google Home as well.
I would like to know if it's possible to do such a thing with my native app and my Google Smart Home action.
This feature is not currently available publicly, it is being tested with a few early partners. I would recommend monitoring our social channels so you can be notified when a feature like this becomes available to everyone.