Is it possible to set the $stageVariable on API Gateway per request? As in, set the Stage Variable Value when the request is made, so that it can be customized per request?
This is what I'm referring to when referring to "stage variable": https://docs.aws.amazon.com/apigateway/latest/developerguide/aws-api-gateway-stage-variables-reference.html
No, as the name implies, stage variable are set on a per stage basis.
They cannot be customized on a per request basis.