Components.AI: Design the composable composer API

### Is your feature request related to a problem? Please describe the problem. Raw leading/trailing fragments do not compose safely with built-in controls, and the public shape for ordered input parts is unresolved. ### Describe the solution you'd like Resolve and review the API for the three-band composer, top/bottom sections, inline leading/trailing contributions, and composer context. Decide between named slots, ordered collections, or registration while preserving defaults and responsive overflow behavior. ### Additional context Leaf task for #68227 requirements C1, C3, and C8 and open design decision 1. Public API review is required before implementation.