Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a zero-parameter, read-only auth check with no output schema and annotations covering the safety profile, the description supplies the essential context (what is checked, where the key comes from, that it is free). The only omission is any hint about the shape of the result, which is a minor gap given no output schema exists.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.