You will need a valid payment method even if the apps are free. You will not be charged for downloading a free app but if:
- the app offers a free trial and you do not cancel 24 hours before it ends, then you will be charged.
- the app offers in-app purchases, a payment method would be needed in case you want to use one of those.
Microsoft Co-Pilot does have in-app purchases.
All downloads will be disabled if you currently have a charge that has not been paid for. Some users have removed their payment method thinking they will not be charged when a free trial ends only to find out that the charge does not go away. When they add a payment method the card will be charged for the money you owe. You may want to contact Apple directly if there is a problem with your billing method.
Contact Apple for support and service - Apple Support