Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a zero-parameter status-check tool, the description is minimal but not entirely inadequate. However, without an output schema or annotations, the agent has no information about the shape of the auth status result, possible states, or failures. Given the existence of sibling tools that require authentication, knowing how to interpret this result is important, and this description leaves that unspecified.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.