Motion AI Full Integration (Calendar, Tasks, Inbox, Schedules)

End-to-end, deterministic integration playbook for the Motion API across v1/v2/v3: verified handshake, calendar orchestration (including external calendars via /v2/calendar-events/search), full CRUD for tasks/projects with AI-driven parameter inference + Babbage Standard metadata, UI-less Inbox triage via unscheduled-task protocol, and availability verification via v1 schedule endpoints with two-failure fallback controls and post-mutation verification reads.