fix(codex): replace dead --enable web_search_cached flag with --search

[kinoko-studio]

Summary

• codex-cli 0.144.1 marks web_search_cached deprecated (codex features list) and prints, on every invocation that still passes --enable web_search_cached:

  deprecated: `[features].web_search_cached` is deprecated because web search is enabled by default.
  Set `web_search` to "live", "indexed", "cached", or "disabled" ... in config.toml if you want to override it.
  

• Live-tested: codex exec with no search-related flag at all still performs real web searches successfully. So the old flag wasn't keeping search on — it was just inert, printing a noisy warning on every gstack codex pass (autoplan, codex, design-consultation, design-review, document-release, office-hours, plan-ceo-review, plan-design-review, plan-devex-review, plan-eng-review, review, ship, plus two scripts/resolvers/*.ts files and the .tmpl counterparts).
• This PR replaces the dead flag with --search rather than dropping it outright (see Drop deprecated --enable web_search_cached from codex calls #2224 for the bare-removal alternative). Rationale for the explicit flag over relying on codex's implicit default: codex-cli has already changed this exact mechanism once (the old features.web_search_cached boolean → the new web_search config key), so pinning search on explicitly is more robust to it changing again than depending on whatever the built-in default happens to be.
• Also corrects the "Web search" doc note in codex/SKILL.md(.tmpl), which described the old flag as "OpenAI's cached index" — inaccurate for --search's live lookup via the native Responses web_search tool.

Test plan

• Verified web_search_cached is deprecated via codex features list and the live stderr warning on codex-cli 0.144.1
• Verified codex exec performs successful real web searches with no search flag at all (rules out "the old flag was required for search to work")
• grep -r "enable web_search_cached" returns zero matches post-fix
• Confirmed --search is present at every prior call site
• bun test test/host-config.test.ts (golden-file regression) — green
• Full bun test browse/test/ test/ make-pdf/test/ ... — exit 0
• bun run skill:check clean across all host targets after bun run gen:skill-docs --host all

Supersedes #2224 (bare removal) — closing that one with this rationale.

🤖 Generated with Claude Code

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