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.

Start with the requirements in #68227, especially C1, C3, and C8, and review open design decision 1. Compare named slots, ordered collections, and registration for the three-band composer, sections, inline contributions, and composer context. Done means a reviewed public API decision that preserves defaults and responsive overflow behavior.

Written by the indexing model from the issue text.