Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (2 params, no nested objects, output schema present), the description is complete enough. It covers the main use case, the authentication context, and a behavioral nuance. The output schema likely describes the return value, so the description doesn't need to. Slight gap: it doesn't mention what happens if the property is not in the list, but that's not critical.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.