Stitch iOS and Android apps include mobile push notifications. These notifications mirror web browser and desktop app notifications settings by default.
Importantly, you will only receive a mobile push notification when you are not online (i.e., on the web app or desktop app).
You can click the notification card and the app will automatically open on your phone, taking you to the unread message.
Please note that mobile push notifications are separate from in-app badges and room name bolding.