Refactor TUI app module into submodules

[etraut-openai]

Why

The TUI app module had grown past the 512K source-file cap enforced by CI/CD. This keeps the app entry point below that limit while preserving the existing runtime behavior and test surface.

What changed

• Kept the top-level App state and run-loop wiring in tui/src/app.rs.
• Split app responsibilities into focused private submodules under tui/src/app/, covering event dispatch, thread routing, session lifecycle, config persistence, background requests, startup prompts, input, history UI, platform actions, and thread event buffering.
• Moved the existing app-level tests into tui/src/app/tests.rs and reused the existing snapshot location rather than adding new tests or snapshots.
• Added module header comments for app.rs and the new submodules.

Follow-up

A future cleanup can move narrow unit tests from tui/src/app/tests.rs into the specific app submodules they exercise. This PR keeps the existing app-level tests together so the refactor stays focused on the source-file split.

Verification

• cargo test -p codex-tui --lib app::tests::agent_picker_item_name_snapshot
• cargo test -p codex-tui --lib app::tests::clear_ui
• cargo test -p codex-tui --lib app::tests::ctrl_l_clear_ui_after_long_transcript_reuses_clear_header_snapshot
• just fix -p codex-tui

Full cargo test -p codex-tui still fails on model-catalog drift unrelated to this refactor, including stale gpt-5.3-codex/gpt-5.1-codex snapshot and migration expectations now resolving to gpt-5.4.