Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the zero-parameter schema and no output schema, the description covers the essential context: what this tool reports, when to call it, and a behavioral note about unauthenticated sessions. It could slightly expand on what the response looks like, but the pointer to 'the response tells you exactly how' is a pragmatic and sufficient signal.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.