iPhone 13 Pro wiht ios16.2 requires restart each time to access App Store

Check the network connection:

You need to have a good Service and/or Wi-Fi.

If they are On, turn Off Hotspot & VPN.

Charge the battery > 70%.

See also ⤵️

1.

If you can't connect to the App Store, iTunes Store, or other Apple services

If you can't connect to the App Store, iTunes Store, or other Apple services - Apple Support

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Make sure that your device is connected to the internet

Use any web browser to connect to any website. If nothing loads, use another device on the same network to see if it can connect to any website. If no other devices can access the internet, turn off your Wi-Fi router, then turn it on again to reset it. If you still can’t connect to your Wi-Fi network, contact your internet provider for more help. If only your first device can’t connect to the internet, get help with Wi-Fi on your iPhone or iPad, Apple Watch, Apple TV, or Mac.

If you use cellular service to connect to the internet on your iPhone or iPad, make sure that you have cellular data turned on for the app that you're using. To do this, open the Settings app, tap Cellular, then turn on Cellular Data.

-> If you tried all of the above steps and you still can’t connect, contact Apple Support.

2.

Check if this helps: Clear the history and cookies from Safari on your iPhone, iPad, or iPod touch

Clear the history and cookies from Safari on your iPhone, iPad, or iPod touch - Apple Support

3.

If an app on your iPhone or iPad stops responding, closes unexpectedly, or won’t open

If an app on your iPhone or iPad stops responding, closes unexpectedly, or won’t open - Apple Support

Do you still get the spinning icon?

Try do a force restart -> Force restart iPhone – Apple Support (UK)

I understand that.

Get more help and assistant from Apple directly, see Contact Apple for support and service -> Contact Apple for support and service – Apple Support (UK)