Which failure should send a message to the dead-letter queue immediately instead of retrying it with backoff?

"The payload fails schema validation because a required field is missing" is correct. A malformed payload fails in the same way on every attempt. Retries only waste time and delay other messages.

The other failures are transient, which means temporary:
• "The database returned a connection timeout"
• "A downstream API responded with HTTP 503"
• "A deadlock was detected and the transaction was rolled back"

The same message usually succeeds a little later. So these deserve retries with backoff before you give up.