Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
Annotations already declare readOnlyHint, idempotentHint, non-destructive and closed-world, so the safety profile is covered. The description adds genuinely new behavioral context beyond them: that the tool returns signup URLs and that the student registers on that page themselves, which tells the agent not to look for an enrollment tool. It does not say how many items come back or whether results are ordered by date.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.