Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (no parameters, read-only, no output schema), the description fully covers the expected behavior: it distinguishes between the connected state and the missing-credentials state, and mentions both the toolkit and per-install URLs. There are no other scenarios or edge cases that need explanation. The description is complete for its purpose.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.