POST /api/v2/conversations/webchat/{id}/messages returns 400 for canned response template

We are attempting to inject a canned response into an active Webchat session via the Conversations API. The POST to /api/v2/conversations/webchat/{conversationId}/messages fails with a 400 Bad Request when we include the templateId in the payload. The documentation is vague on the required structure for templateId. The request body looks like this:

{
 "templateId": "abc-123-template",
 "templateVariables": {
 "name": "User"
 }
}

The error response returns invalid_request_body. What is the correct JSON schema for sending a canned response template through this endpoint?