Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a no-parameter, read-only status tool, the description covers all essential aspects: what it returns, the two main scenarios (authenticated vs. missing creds), and the meaning of fields like 'connect_url'. There is no output schema to compensate for, but the description fully specifies expected behavior.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.