They tell you the fix: 401 means check your token, 403 names the missing scope, 429 carries Retry-After and rate-limit headers, and 503 means the external API is not enabled yet, mint a token in the Developer Portal.
The 503-when-off behavior is worth knowing: it distinguishes 'turn the API on' from 'your token is wrong,' which saves the classic first-integration debugging hour.
Both SDKs surface these as typed errors with the hint in the message.