Thank you for reaching out.
I understand that you were not charged for your Azure Basic Public IP address before May 29th 2024 but you are able to see charge 0.004/hour rate on your billing statement.
As your issue is related to billing of a resource, the correct approach here will be to create a Billing Support Ticket with Azure. Azure provides free billing support to all azure customers. You can follow the documentation here and create a support ticket of type Billing.
Just an FYI On 30 September 2025, Basic SKU public IP addresses will be retired in Azure unless the Basic SKU public IP addresses deployed in Azure Cloud Services (extended support) those deployments will not be affected. More details can be found here.
Hope this helps. Please let me know if you have any additional questions. Thank you!