What JSON data is sent to the webhook URL for Environment Deployment Notifications? I'm trying to find out what key values are available to use in the message template? The documentation for build notifications seems to be pretty thorough (https://www.appveyor.com/docs/notifications/#webhook-payload-default), but I can't find similar information for the environment deployments.
Build notification webhook data you mentioned is subset of it. It also contains some data related to specific environment deployment. We recently filed https://github.com/appveyor/ci/issues/1531 to document it.
For now you can create request bin at http://requestb.in and use it for experiment and see that content.