Refactor chatwidget settings surfaces into modules (phase 4)

[etraut-openai]

Why

chatwidget.rs is still carrying too many unrelated responsibilities in one file. #22269 started a five-phase cleanup to move coherent behavior domains into focused modules while keeping chatwidget.rs as the composition layer. #22407 completed phase 2 by extracting input and submission flow, and #22433 completed phase 3 by extracting protocol, replay, streaming, and tool lifecycle handling.

This PR is phase 4. It keeps moving high-churn UI coordination out of the central widget by extracting settings, popups, and status surfaces without changing the visible behavior those flows already provide. This is once again a mechanical movement of existing functions. No functional changes.

What Changed

• Added focused modules for runtime settings/model coordination, model/reasoning/collaboration popups, settings/personality/theme/audio/experimental popups, permission prompts, status setup/output controls, and Windows sandbox prompt flows.
• Moved the remaining rate-limit nudge/status helpers and connectors popup/loading/update helpers into their existing focused modules.
• Preserved the existing picker flows, approval behavior, status/title setup previews, rate-limit notices, and connectors/app list behavior while shrinking chatwidget.rs back toward orchestration.
• Left codex-rs/tui/src/chatwidget.rs as the registration and composition surface for these extracted behaviors.

Cleanup Phases

The five-phase cleanup plan from #22269 is:

1. Phase 1: mechanical helper and state moves. Completed in Refactor chatwidget state into modules #22269.
2. Phase 2: extract input and submission flow, including queued user messages, shell prompt submission, pending steer restoration, and thread input snapshot/restore behavior. Completed in Refactor chatwidget input flow into modules #22407.
3. Phase 3: extract protocol, replay, streaming, and tool lifecycle handling, while preserving active-cell grouping, transcript invalidation, interrupt deferral, and final-message separator behavior. Completed in Refactor chatwidget protocol flows into modules (phase 3) #22433.
4. Phase 4: extract settings, popups, and status surfaces, including model/reasoning/collaboration/personality popups, permission prompts, rate-limit UI, and connectors helpers. This PR.
5. Phase 5: clean up the remaining constructor and orchestration code once the larger behavior domains have moved out, leaving chatwidget.rs as the composition layer.

Verification

• cargo check -p codex-tui
• cargo test -p codex-tui chatwidget::tests::permissions
• cargo test -p codex-tui chatwidget::tests::status_surface_previews
• cargo test -p codex-tui chatwidget::tests::popups_and_settings
• cargo test -p codex-tui chatwidget::tests::status_and_layout

cargo test -p codex-tui also compiles and begins running, but aborts in the unchanged app-side test app::tests::discard_side_thread_keeps_local_state_when_server_close_fails with a reproducible stack overflow.

[canvrno-oai]

Same review process as the other mechanical PRs that are a part of this series- spot checked a few functions on chatwidget.rs to confirm they were moved elsewhere, asked Codex to review, and compiled locally.