How do I update my App Store account email on iPhone 14?

Are these brand new apps that you've never downloaded before? Or are you updating or redownloading apps?

An App Store app is tied to the Apple Account used to acquire it (paid or free). The Apple Account is encoded into the licensed copy that is downloaded. It is in the copy's DNA. That is the only Apple Account that can redownload or update the app.

The situation you describe can happen if there are apps (or media purchases) on the device that were installed (or downloaded) under a different Apple Account, and they need updating or redownloading. This can sometimes happen if you "change" the email address for your Account improperly and you instead create a brand new Apple Account.

You can migrate the content from the original account that acquired it to another Apple Account*;

Migrate purchases from one Apple Account to another Apple Account - Apple Support

*This feature isn’t currently available to users in the European Union, United Kingdom, or India. Users in these countries will have to reacquire content, which may include repurchasing or set up a Family Sharing situation between the two accounts.

M1 Mac mini, macOS 15.5;  Watch, series 10 GPS-only, watchOS 11.5; iPhone 16, iOS 18.5; TV 4th Gen, tvOS 18.5 HomePods, audioOS 18.5