When I send an actionable message containing a card with "autoInvokeAction", it doesn't appear in the message in Outlook. It just comes through set to null.
However, the confusing thing is that when I send the exact same card JSON using the site https://amdesigner.azurewebsites.net/, it does appear in the body.
Why would my outgoing email be treated differently from the AMDesigner?
I found the answer today by getting in touch with Microsoft Support. The actionable messages team has to approve the sender for the auto-invoke capability. It doesn't work by default. This isn't documented.