API Gateway API log groups or streams can only be deleted and recreated by redeploying the API

AWS Security Token Service(STS) is used by API Gateway for logging data to CloudWatch logs. Hence, AWS STS has to be enabled for the Region that you're using

You are charged for accessing method-level and stage-level CloudWatch metrics, but not for API-level metrics

To enable CloudWatch Logs for all or only some of the methods, you must also specify the ARN of an IAM role that enables API Gateway to write information to CloudWatch Logs on behalf of your user. The IAM role must also contain the following trust relationship statement

In access logging, only $context and$input variables are supported