By default, Google Cloud Pub/Sub Push Subscriptions deliver a message to a push endpoint as a Wrapped message in the following (abbrievated) format

{
    "message": {
        "data": string,
        "messageId": string,
        "message_id": string,
        "publishTime": string,
        "publish_time": string
    },
    "subscription": string
}

This is hidden in the Push Subscription documentation and not surfaced in the PubsubMessage reference documentation which shows the following format:

{
  "data": string,
  "attributes": {
    string: string,
    ...
  },
  "messageId": string,
  "publishTime": string,
  "orderingKey": string
}

I haven't verified, but I suspect that the configuration for choosing unwrapped messages is to Enable payload unwrapping

Have you used Cloud Run with Pub/Sub and ran into this? Let me know in the comments.