Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
With no output schema, the description covers the main return scenarios and clarifies pending[], authenticated, and connect_url behavior. It is slightly thin on the exact authenticated value and pending contents in the partially connected/missing-credentials case, but it is adequate for a zero-parameter status tool.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.