I'm doing a POST to https://iap.googleapis.com/v1/projects/MY_PROJECT_ID/iap_web:getIamPolicy with an empty body as the documentation specifies.
The API response is an HTTP 200 with the body simply being {"etag": "ACAB"}
What does this mean? What should I be doing differently to retrieve the actual policy data?
IAP and the IAP API are both enabled for this project.
The issue is that your URI is not specifying the Resource Type, which can be app-engine or backend-services.
For App Engine change the URI to:
https://iap.googleapis.com/v1beta1/projects/PROJECT_NUMBER/iap_web/appengine-PROJECT_ID:getIamPolicy?alt=json