What are data transfer rates between EC2, Fargate, or Lambda to App Runner?

Hello.

AppRunner's documentation states that it is free within the same region.
https://aws.amazon.com/ecr/pricing/?nc1=h_ls

Data transfer “in” and “out” refers to transfer into and out of Amazon ECR. Data transferred between Amazon ECR and other services within the same Region e.g., Amazon EC2, AWS Lambda, AWS App Runner, or AWS Fargate is free of charge (i.e., $0.00 per GB). Data transferred between Amazon ECR and other services in different regions will be charged at Internet Data Transfer rates on both sides of the transfer.

The EC2 documentation states that if you cross Availability Zones within an AWS region, you will be charged $0.01, but this may not be included in the case of AppRunner.
https://aws.amazon.com/ec2/pricing/on-demand/?nc1=h_ls#Data_Transfer_within_the_same_AWS_Region

I recommend that you open a case with AWS Support under "Account and billing" just to be safe.
Inquiries under "Account and billing" can be made free of charge.
https://docs.aws.amazon.com/awssupport/latest/user/case-management.html