Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (no parameters, no output schema, annotations cover safety), the description does a solid job explaining the two main return scenarios. It lacks a comprehensive schema of return fields, but for a status-checking tool, the provided details about authenticated, pending, and URLs are adequate. It could be more complete by describing partial connectivity, but the essentials are covered.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.