Paying for an app subscription late is not, by itself, what prevents you from downloading apps from the App Store. These are two separate issues.
If your payment for a particular app subscription is late or has failed, the usual consequence is that access to that particular subscription or its premium features may be restricted. It does not normally mean that you are prevented from downloading every other app from the App Store. In other words, a late subscription payment for one app should not be confused with a general App Store download restriction.
If you are unable to download even free apps, that strongly suggests there may be an issue with the payment method or billing status associated with your Apple Account (Apple ID). For example, there could be an unpaid balance, a declined payment, or no valid payment method available on the account. In such circumstances, Apple may restrict new purchases and downloads, including downloads of free apps, until the billing issue is resolved.
Therefore, the fact that a subscription payment was made late does not, by itself, explain why you cannot download apps from the App Store. Check Settings > [your name] > Payment & Shipping and look for any billing alert, declined payment, or outstanding balance associated with your Apple Account. Resolving that billing issue should restore the ability to download apps, subject to any other restrictions on the account.
If you can't download, make purchases, or update apps, including free apps, you must update your payment method or add a new one. If you verified that a payment method is available in your country or region and you're still having trouble, learn more.