An API free trial credit expires three months after account creation, and is only created on the first account per phone number.
If your trial is in effect, you don’t have to add a payment method to make (rate-limited) API requests.
You can see an operational trial grant under an account’s “usage” for older accounts (like shown in the first post), or now trial balance in big text under the main “billing” screen for new accounts without prior payment method.
The prepaid credit system is now required for new API accounts to convert to paid use - and older accounts in case you remove all existing payment methods.