Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
Annotations already declare destructiveHint=true, idempotentHint=true, readOnlyHint=false, so the mutation safety profile is covered by structured data. The description adds a real behavioral constraint not in the annotations: foreign notification IDs are rejected, i.e. ownership/authorization is enforced. It does not add anything on idempotency or response behavior, but that is already structured.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.