Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (one parameter, no output schema, idempotent and non-destructive annotations), the description covers the essential semantics: the action and the required state. It could be more explicit about behavior if the channel is already running, but the idempotent annotation and STOPPED-status condition provide sufficient context for an agent to select and invoke the tool correctly.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.