Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a zero-parameter, no-annotation, no-output-schema tool, the description is largely complete: it says what is deleted, in what scope, and what is not deleted. An agent may need to infer that subsequent tool calls will require reauthentication, but that follow from the stated clearing of cookies and tokens and does not make the description inadequate.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.