Is it possible to make your Discourse site into a native app on Google Play Store and the App Store? Not an app with a built-in browser
Anything is possible given infinite time and money!
The non-snarky version:
The frontend and backend of Discourse are separate enough that you could hire someone to build a native app and they wouldn’t have to make any changes to the backend. Though it wouldn’t work very well with themes and plugins that patch the current one.
And it isn’t going to happen until someone pays for it. Everyone seems to prefer spending their money on improving the web page.