Can’t update or download without payment method, I have no such method

I can’t select NONE, the option does not exist

If you want to make purchases or update / download apps, including free apps, you need to have a payment method on file.

If you don't have a credit card or don't want to use a credit card, you can also use your Apple ID balance as payment method, see -> Add money to your Apple ID balance

Add money to your Apple ID balance – Apple Support (UK)

See also: 

What you can buy with your Apple Gift Card or Apple ID balance

What you can buy with your Apple Gift Card or Apple Account balance – Apple Support (UK)

How to redeem your Apple Gift Card or App Store & iTunes gift card

How to redeem your Apple Gift Card or App Store & iTunes gift card – Apple Support (UK)

When redeeming a gift card, (1) the amount will be credited to your Apple ID balance and (2) then you need to set your Apple ID balance as your default payment.

(1) See -> Check your Apple ID balance

Check your Apple ID balance – Apple Support (UK)

(2) See -> Add a payment method to your Apple ID

Add a payment method to your Apple ID – Apple Support (UK)

If you update your payment method or add funds to your Apple ID balance, It would take about 1 to 3 business days in order to process.

If you're still unable to update your payment method, Contact Apple Support.

Read also the articles below ⤵️

If you can't redeem your Apple Gift Card or App Store & iTunes Gift Card

If you can't redeem your Apple Gift Card or App Store & iTunes Gift Card - Apple Support

• You can't redeem Apple Gift Cards or App Store & iTunes Gift Cards outside the country or region of purchase. For example, if you bought an App Store & iTunes Gift Card in France, you can't redeem it in the App Store in the United States.

About Gift Card Scams -> About Gift Card Scams - Official Apple Support