I can't download apps from the App Store because I need to change my payment method

See this article about updating payment methods on various platforms (iPhone, Mac, etc.): If you need to change or update your Apple ID payment method - Apple Support

Also note: "If you change your address, the credit or debit card information that you use with your Apple ID might be automatically updated by your financial institution, and you don't need to take action. But if there's an issue [such as you having a subscription or being a Family Sharing Organizer], add a new card first, then remove the old card."

You usually need a payment method -

You usually need to have added a valid payment method to your account. Even to re-download or update apps and for free apps. You can find the acceptable payment methods for your country here;

Payment methods that you can use with your Apple ID - Apple Support

M1 Mac mini, macOS 14.2;  Watch, series 7 GPS/cellular, watchOS 10.2; iPad Pro 2nd Gen, iPadOS 16.7.3; iPhone 12 Pro, iOS 17.2; TV 4th Gen, tvOS 17.2; HomePods, audioOS 17.2 and Airport Express w/ Airplay 2