When calling a Function App that returns a 202 (Accepted) Status Code I found my HTTP action in my Logic App was returning a status code of 405 with the a message of “The HTTP ‘GET’ method is not supported by the ‘GenericJsonWebHookReceiver’ WebHook receiver.”.
This seemed a bit odd because I had tested my Function App using the exact same request using Postman and it was returning a valid 202 response. After reading a bit more about HTTP Actions (https://docs.microsoft.com/en-us/azure/logic-apps/logic-apps-workflow-actions-triggers#http-action) the section on Asynchronous Patterns gave me the answer. To disable the asynchronous behavior previously described, set operationOptions to DisableAsyncPattern in the action inputs. In this case, the action’s output is based on the initial 202 response from the server.
Having made this change to the Logic App the server response was accepted and considered a success.