My phone.

Hi Valsnyde

Welcome to the Apple (user-to-user) Community.

Seems you are having no success in upgrading or downloading apps.

Thank you for letting us know your iPhone model, and iOS version.

Wondering if you are signed in (to your device) with your Apple ID.

How to: Sign in with your Apple ID - Apple Support

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For iPhone iOS : Seems iPhone 7 Plus is not compatible with iOS 16

About iOS 15 Updates - Apple Support says iOS 15.7.3 is recommended:

How to: Update your iPhone or iPad - Apple Support

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For App Store apps:

Check if iPhone settings have a restriction on purchases:

Manage App Store purchases, subscriptions, settings, and restrictions on iPhone – Apple Support

How to: Get apps in the App Store on iPhone – Apple Support

What to do:

If you can’t download or update apps on your iPhone or iPad - Apple Support

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If needed:

App Store Support has a website online.

App Store - Official Apple Support

All the best :-)