Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a zero-parameter, read-only status tool with no output schema, the description fully covers the return behavior in both relevant states: connected and missing credentials. It also mentions the specific fields returned (authenticated, pending[], connect_url, per-install URLs), making it complete for the tool's complexity.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.