How do I update apps without the App Store

Hello,

It appears you may not be able to find your App Store app. This issue is outlined in this support article --> Download apps and games on your iPhone or iPad - Apple Support

Certain built-in apps cannot be deleted so it is somewhere on your device. It can be hidden by you, or by an administrator if your device is managed by an education or business institution. In the latter case you need to contact the administrator.

See if you hid it with restrictions:

Screen Time - Allowed apps Use parental controls on your child's iPhone, iPad, and iPod touch - Apple Support

- "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] - Organize the Home Screen and App Library on your iPhone - Apple Support

"Search for it ( Use Search on your iPhone, iPad, or iPod touch - Apple Support ). Swipe down from the middle of any home screen and type the name of the app 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] 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."