To launch a specific Telegram Mini App just like a regular Android/iOS app, you can save its icon to your home screen, as shown in the image below.
Fig. 1. Example icon of the Telegram app “Book Store”.
Setup
To save the app icon to the home screen on mobile devices:
Open the desired app.
Fig. 2. Any screen of the app.
Tap the three dots in the top right corner.
Fig. 3. Three dots in the top right corner.
From the dropdown menu, select “Add to Home Screen”.
Fig. 4. The menu item you need.
4. Done! The icon is now on your home screen.
Fig. 5. Example of the app icon on the home screen.
Tapping it will immediately launch the selected app in Telegram.
You can also move the icon around and group it with other app icons, just like any regular app.