Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no parameters, no output schema, and supporting annotations (readOnly, idempotent, non-destructive), the description is sufficient. It explains the return behavior in both states (authenticated vs missing credentials), which is the key contextual information an agent needs. Could mention how the connect_url is used, but not critical.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.