Don’t have credit card for more storage

See this Apple article: Change, add or remove Apple ID payment methods

https://support.apple.com/en-gb/HT201266

You are right. If you do not have enough storage space on iCloud, then you cannot backup your iPhone to iCloud. As you know, you will have to purchase a higher iCloud capacity subscription.

You have discovered that you need a valid credit/debit card listed in the payment method as well.

Axel F.