Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
Annotations already declare readOnlyHint, idempotentHint, and destructiveHint=false. The description adds useful behavioral detail: the exact return conditions for authenticated:true vs connect_url and per-install URLs. It does not mention possible partial-connection states, but for a simple status tool this is sufficient.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.