Components.AI composable composer

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

The current message input exposes raw fragments that replace defaults accidentally and does not provide reusable, context-aware input parts.

### Describe the solution you'd like

Track the API design and implementation of a three-band composable composer, cascading composer context, reusable controls, correct send/stop behavior, keyboard and IME handling, autogrow, limits, and draft preservation.

Attachments, voice, suggestions, and queueing should consume this composition model through separate workstreams.

This is a workstream under #68227. Its independently mergeable tasks are represented as native sub-issues.

### Additional context

Covers requirements C1-C3, C5-C8, C10, H1-H2, and relevant interaction-state requirements from #68227.

Start with parent issue #68227 and its native sub-issues, since this workstream is explicitly divided into independently mergeable tasks. Review requirements C1-C3, C5-C8, C10, H1-H2 and the referenced interaction-state requirements. Done means the composable composer model and its listed behavior are covered by those tasks; no implementation file or test is named here.

Written by the indexing model from the issue text.