Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
Goes beyond annotations by reporting a concrete rate limit (10/hour/account), scoping the external effect ("reads your public pages; nothing on your site changes") and disclosing that a record is persisted in the account, which is consistent with readOnlyHint=false and idempotentHint=false. It does not say whether the check completes synchronously or must be polled via get_site_check, which is the main remaining behavioral gap.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.