Components.AI suggestions experience

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

Suggestions currently send immediately, appear only before the first turn, and are not modeled as a reusable composer-adjacent part.

### Describe the solution you'd like

Track suggestion behavior that fills the composer without submitting, remains available during conversations, respects interaction state, and can be supplied dynamically by an agent.

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

### Additional context

Covers C9 and K1-K5 from #68227.
See: https://github.com/dotnet/aspnetcore/pull/68333#issuecomment-5413299117

Start by reading parent issue #68227 and its native sub-issues, then review the linked discussion in PR #68333. Use the C9 and K1-K5 requirements to identify the independently mergeable work; done means suggestions fill the composer without submitting, remain available during conversations, respect interaction state, and can be supplied dynamically by an agent.

Written by the indexing model from the issue text.