Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a parameterless status tool, the description covers the main behavioral branches well. It could go slightly further by specifying the full response shape (e.g., what fields constitute the connection status, the structure of pending[]), but it places the key details about what happens in each state. Given no output schema exists, the description carries the return-format burden adequately.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.