fix: preserve Codex composer on skin new-chat drafts

[Rat0323]

Summary

• Preserve Codex's native composer and home geometry for transient projectless and project "new chat" drafts when a skin is active.
• Gate fixed-height/hero layout rules on the classic home chrome, and mark non-classic routes as soft instead of applying the structured layout.
• Apply the runtime/CSS fix across Dream Skin, Cidala Tiger, Snow Skin, and the central custom skin path on Windows and macOS.
• Add manager and Rust regression coverage.

Fixes #1596

This PR is based on main at v1.2.44 (77091cc) and intentionally does not include the unrelated changes from PR #1712.

Verification

• npm test — 37 passed
• node --check — all modified renderer bundles pass
• cargo test -p codex-plus-core --test cdp_bridge — 93 passed
• cargo test -p codex-plus-core --test dream_skin_runtime — 9 passed, 1 ignored (live renderer test)
• cargo test -p codex-plus-core --test upstream_theme_assets — 2 passed on LF-normalized assets
• git diff --check — clean