Below is the link that mentions all the methods and you can also use them in your current account, however, there are no other mechanisms than these to capture App-runner logs. However, App Runner is integrated with AWS CloudTrail, a service that provides a record of actions taken by a user, role, or an AWS service in App Runner. CloudTrail captures all API calls for App Runner as events.
You can view the most recent events in the CloudTrail console, and you can create a trail to enable continuous delivery of CloudTrail events to an Amazon Simple Storage Service (Amazon S3) bucket.
You can also reach out to AWS Premium Support for more details and information and confirm if there are any internal tools that the Support Team has access to which can provide more detail.
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