So one thing nice about this forum and the software used is you can make it appear and act like a phone app without actually installing it as an app. There’s actual Discourse Apps out there but from what I’ve seen and read, most claim they’re not as good as simply doing the following steps to make it appear as an app on your phone or tablet.
If you’re on a Android, you can simply load the site in Chrome. Once loaded, you can open the Chrome Menu (3 dots on upper right of window) and simply click “Add to Home Screen”.
If you are on iPhone or IOS, you’ll have to do the same steps within Safari.