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, read-only, clear output states), the description provides all necessary context. The annotations cover safety and idempotency, while the description explicitly details the return values and the conditions that trigger different responses. The absence of an output schema is adequately compensated by the description's mention of key fields like authenticated, pending, and connect_url.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.