Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a single-parameter read-only tool with no output schema, the description covers the purpose, when to call, auth, and the key status value. It does not enumerate all possible statuses or the return format, but for a minimal check tool this is likely sufficient. There is no output schema to rely on, so a slightly richer description of possible statuses could improve completeness.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.