tui: split remaining composer draft and footer state

[etraut-openai]

Why

#22581 started separating the chat composer’s responsibilities, but ChatComposer still owned the remaining editable draft state alongside footer/status presentation state. This follow-up makes those ownership lines explicit so future composer changes have a smaller blast radius and BottomPane does not need to keep exposing scattered draft getters.

This is just a refactor. No functional or behavioral changes are intended.

What changed

• Move the remaining editable composer state into bottom_pane/chat_composer/draft_state.rs.
• Move footer and status-row presentation state into bottom_pane/chat_composer/footer_state.rs.
• Add an internal ComposerDraftSnapshot for restore flows, replacing several ad hoc BottomPane pass-through reads.
• Rewire the related history-search and thread-input restore paths to use the extracted state.

Verification

• RUST_MIN_STACK=8388608 cargo test -p codex-tui
• cargo insta pending-snapshots

[fcoury-oai]

Smoke tested the draft and footer behavior.

Looks good, approved.