Components.AI: Implement composer sections and cascading context

### Is your feature request related to a problem? Please describe the problem.

Applications cannot arrange reusable input parts without replacing built-in behavior or reimplementing composer state integration.

### Describe the solution you'd like

Implement the approved three-band composer API and cascade current text, attachments, busy/can-send state, and submit/cancel commands to built-in and app-supplied parts. Empty attachment bands must not render.

### Additional context

Leaf task for #68227 requirements C1, C3, and C8. Depends on approval of the composer API.

Start by reading the parent issue #68227, especially requirements C1, C3, and C8, and confirm the composer API is approved. Then trace the Components.AI composer entry points and determine how the three bands should cascade text, attachments, busy/can-send state, and submit/cancel commands. Done means built-in and app-supplied parts receive that context and empty attachment bands do not render.

Written by the indexing model from the issue text.