Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool has no input schema, no output schema, and simple read-only behavior, the description is complete. It covers both success and failure modes, including the structure of the response (authenticated, pending[], connect_url) and the addition of per-install URLs when credentials are missing.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.