Hi - I had the exact same problem. The reason the App Store isn't showing (and you're receiving the "Can't open Safari" error message is due to your screen time settings. You have to make sure iTunes Store and/or App Store purchases are "Allowed."
Go to Settings -> Screen Time -> Content & Privacy Restrictions. Next, tap Allowed Apps. Make sure the switches next to Safari, iTunes Store, and Camera are turned on.
If you believe you deleted the App Store, go back to Settings -> Screen Time -> Content & Privacy Restrictions. Then, tap iTunes & App Store Purchases. Make sure it says next to Install Apps, Deleting Apps, and In-app Purchases. If one of these options says Don’t Allow, tap on it, then tap Allow. Here are the full instructions:
https://www.payetteforward.com/i-deleted-app-store-safari-itunes-camera-from-my-iphone-ipad-pod-heres-the-real-fix/
This should fix it, just fixed my wife's iPhone 6 by following the above steps.