Can’t download apps in App Store

You can set up your Apple ID without a payment info, but you'll need to use iTunes Gift cards, to have at least credit to theoretically buy an app, even if the download is for free.

Create or use an Apple ID without a payment method - Apple Support

Did you check, if your payment info is still correct, and that there is enough iTunes credit, to buy or download apps?

Change, add, or remove Apple ID payment methods - Apple Support

Any error messages given?

Apple still requires some method of payment. Even for free apps.

So, your only other option is Ingo271’s method of purchasing and using iTunes Gift Cards and register the cards using the registration code on the back.

Apple will not let anyone use/download apps or any other free media from any of its stores, unless there is a valid form of payment in place.

Sorry & Best of Luck to You!