Restore app store to iPad

You can’t delete it so it is somewhere on your device.

You may have restricted it. Check Settings>General>Restrictions and make sure the App Store is not disabled.

Search for it. 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.

You can also 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.

When I swipe down for the search bar and type App Store, nothing comes up. No apps at all.

Do you have Siri Search disabled?

https://www.macrumors.com/how-to/apps-siri-suggestions-ios-11/

Do you have the app restricted?