Split ChatWidget state into focused modules

[etraut-openai]

Summary

ChatWidget has been carrying several independent domains in one large state bag: transcript bookkeeping, turn lifecycle, queued input, status surfaces, connectors, review mode, and protocol dispatch. That makes otherwise-local changes hard to reason about because unrelated fields and side effects live beside each other in chatwidget.rs.

This is the first cleanup PR in a larger decomposition effort. It does not try to make chatwidget.rs small in one sweep; instead, it establishes focused state boundaries that later handler, popup, rendering, and effect-synchronization extractions can build on.

This PR keeps ChatWidget as the composition layer while moving focused state into smaller codex-tui modules. The widget still owns effects that touch the bottom pane, app events, command submission, redraw scheduling, and terminal-title updates.

Changes

• Add focused state modules under codex-rs/tui/src/chatwidget/ for input queues, turn lifecycle, transcript bookkeeping, status state, connectors, review mode, and app-server protocol dispatch.
• Update ChatWidget to hold grouped state structs and route input/lifecycle/status operations through those focused helpers.
• Move app-server notification dispatch into chatwidget/protocol.rs while leaving feature handlers and side effects on ChatWidget.
• Replace the large manual ChatWidget test literal with the normal constructor plus narrow test overrides, so future state moves do not require every field to be restated in test setup.
• Update existing tests to access the new grouped state or narrower helpers without changing snapshot behavior.

Longer-term direction

Follow-up PRs can continue shrinking chatwidget.rs by moving behavior, not just state, into focused modules:

• Extract input/submission flow, turn/stream handling, and tool-cell lifecycles into domain modules that call the new state reducers.
• Move popup/settings builders and rendering helpers out of the main widget file so ChatWidget stays focused on composition.
• Reduce direct BottomPane mutation by applying domain-specific sync outputs at clearer boundaries.