Refactor chatwidget input flow into modules

[etraut-openai]

Why

chatwidget.rs is still carrying too many unrelated responsibilities in one file. #22269 started a five-phase effort to move coherent behavior domains into focused modules while keeping chatwidget.rs as the composition layer.

This PR is phase 2 of that plan. It extracts the input and submission flow as a mechanical move before the later protocol, popup/status, and constructor/orchestration phases.

What Changed

• Added codex-rs/tui/src/chatwidget/input_flow.rs for composer input results, queued user-message draining, pending-input previews, and mode-specific submission entry points.
• Added codex-rs/tui/src/chatwidget/input_submission.rs for user-message construction/submission, shell prompt submission, structured mention resolution, and blocked image draft restoration.
• Added codex-rs/tui/src/chatwidget/input_restore.rs for initial-message submission, pending steer restoration after interrupts, and thread input snapshot/restore behavior.
• Registered the new modules and removed the moved ChatWidget impl methods from codex-rs/tui/src/chatwidget.rs.

Follow-On Refactor Phases

The five-phase plan from #22269 is:

• Phase 1: mechanical helper and state moves. Completed in Refactor chatwidget state into modules #22269.
• Phase 2: extract input and submission flow, including queued user messages, shell prompt submission, pending steer restoration, and thread input snapshot/restore behavior. This PR.
• Phase 3: extract protocol, replay, streaming, and tool lifecycle handling, while preserving active-cell grouping, transcript invalidation, interrupt deferral, and final-message separator behavior.
• Phase 4: extract settings, popups, and status surfaces, including model/reasoning/collaboration/personality popups, permission prompts, rate-limit UI, and connectors helpers.
• 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.