A PWA is not installed (or able to be published) on a device via an app store, that is only available for a native mobile app (or hybrid). If you check the box Allow add to home screen prompt from the application navigation profile, the user will be prompted (depending on browser) to install the app on their device. See the following for more information:
https://docs.mendix.com/refguide/progressive-web-app/#22-allowing-add-to-home-screen-prompt
In the mean time it should be possible to publis it to the Play Store. See https://medium.com/mendix/publishing-a-mendix-pwa-in-the-google-play-store-4084a5530224