How do I get back the App Store?

• Check the App Library.

Find your apps in App Library on iPhone - Apple Support

• Allow Installing Apps at Settings > Screen Time > Content & Privacy Restriction > iTunes & App Store Purchases > Installing Apps. If that does not work, then try turning off Content & Privacy Restrictions completely at Settings > Screen Time > Content & Privacy Restriction > Content & Privacy Restrictions.
• If your device is managed by MDM software used in Work or School environments, then the IT Administrator would need to allow it.

Your best chance may be to reset your phone settings and reset the home screen layout.