Data processing costs of TGW-Cloud WAN mixed setup(Federating Transit Gateways with Cloud WAN)

in the article "https://aws.amazon.com/blogs/networking-and-content-delivery/aws-cloud-wan-and-aws-transit-gateway-migration-and-interoperability-patterns/" Cloud WAN is presented as initially being inserted to provide connectivity between TGW's and job is done.

Federating Transit Gateways with Cloud WAN – In this model you replace statically created Transit Gateway peering connections with Cloud WAN. This results in simple connectivity and global dynamic routing. If you like, you can stop your migration here and use Cloud WAN as a dynamic routing hub for your Transit Gateways.

That works wonders and would be ideal. But I got below feedback as well from AWS. "So with TGW - CWAN - TGW... there's 2 traffic processing charges (as one peering is treated as one, but the other TGW is another resource there). Same as TGW - TGW - TGW" The explanation about costs I could not reference anywhere on a public facing article by AWS.

As amazon states publicly (https://aws.amazon.com/transit-gateway/pricing/) Data processing charges apply for each gigabyte sent from a VPC, Direct Connect or VPN to the AWS Transit Gateway Data processing charges do not apply for data sent from a peering attachment to a Transit Gateway. Data transferred over a peering attachment incurs the standard inter-Region data transfer charges.

But they also stated in direct communication that the "Data processing charges do not apply for data sent from a peering attachment to a Transit Gateway" applies for 2 hops only. So in a TGW-CloudWan-TGW scenario, you have (TGW-no fee-CloudWan)-paid data processing - TGW

So wanted a confirmation if anyone has it in production : do you get charged twice for data processing if you use the "Federating Transit Gateways with Cloud WAN" model?

kind regards.