fix(api): serialize Codex thread settings in config (JAM-232)

[darvell-thenvoi]

Resolves https://linear.app/thenvoi/issue/JAM-232/correct-codex-threadturn-serialization-for-reasoning-effort-and-web

Codex 0.148 reads thread reasoning and web-search defaults from thread/start and thread/resume config. The SDK instead emitted top-level effort and legacy search extras, inherited thread effort into turn/start, and sent unsupported per-turn modelProvider.

This branch first reapplies the previously reviewed native terminal-status patch after the latest fork replay, then corrects request ownership:

• Thread start and resume serialize config.model_reasoning_effort and config.web_search.
• Dynamic tools remain start-only.
• Turn start sends only explicit per-turn effort and no provider or search fields.
• Typed thread settings override duplicate generic config values while preserving unrelated config.
• Public per-turn provider/search fields are removed with migration notes.

Review focus: exact Codex 0.148 field ownership, typed-versus-generic config precedence, and source compatibility for removed per-turn setters.

Verification:

• Four exact serializer regressions fail on the prior pinned implementation, pass on this branch, and fail when only the serializer is reverted.
• cargo fmt --all --check passed.
• The full SDK suite passed: 76 unit, 8 high-level stdio, 4 raw stdio, 7 WebSocket, 8 protocol, and 2 schema tests.
• Direct Codex 0.148 probes accepted start/cold-resume config effort, explicit turn effort, and start-only dynamic tools after capability negotiation.
• Independent review approved the final two-commit diff against jam-owned-stdio-latest.

Jam's dependency pin and real owned-Codex start/resume/web-search journey remain in thenvoi/tjam and are not claimed by this dependency pull request.

[linear-code]

JAM-232