I cannot install the App Store app

You can’t delete the App Store app so it is somewhere on your device.

See if you hid it with restrictions:

Screen Time - Allowed apps https://support.apple.com/en-us/HT201304#allow-apps

- "If you turn off an app or feature, it won’t delete it, it’s just temporarily hidden from your Home screen."

- Settings > Screen Time > Content & Privacy Restrictions > [Enter passcode] > Allowed Apps

See if it is in your App Library -->

Organize the Home Screen and App Library on your iPhone [iOS14] - https://support.apple.com/HT211345

"Search for it ( https://support.apple.com/HT201285 ). Swipe down from the middle of any home screen and type App Store into the search field at the top of the screen. If it is in a folder, it will show the folder on the right of the app name after you tap on the app when it appears in the search."

"Reset the Home screen layout which will return the App Store to the home screen as long as it isn’t restricted. When you do this, it returns the home screen to out of the box condition and it will destroy any folders you had on the home screen. Settings > General > Reset > Reset Home screen layout."

- Updated from April 2018 Apple Recommended post by Demo about a missing App Store app - https://discussions.apple.com/message/33245486#message33245486

The App Store App is an integral element of the Operating System. It cannot be removed, but can be hidden from you if the iPad is centrally managed, or owned, by an Educational establishment or Enterprise.

If your iPad is a managed device, you will need to seek assistance from the System Administrator that manages your device.

In the event that your iPad is not managed by a third-party, then some other explanation will explain the apparent absence of the App Store from your iPad. Perhaps you have moved the App to an App folder? Try using the iPad Search function to find the App Store on your iPad.