fix(codex): preserve search mode and harden Codex workflows

[time-attack]

What it does

Keeps Codex web search working without deprecated flags or silently forcing live browsing, resolves make-pdf correctly from Codex installs, avoids an eval-based path lookup, and validates fenced bash in generated skills.

How it works

Codex invocations now inherit the user's configured web-search mode (cached by default), global browse resolution checks current Codex/agents locations before legacy Claude and PATH locations, gstack-paths --get returns one validated root, and a test runs bash -n over discovered fenced shell snippets.

What was broken

gstack passed a deprecated cached-search feature toggle. The proposed --search replacement would have changed cached search to live search. make-pdf could skip the active Codex browse installation, /codex needed to evaluate assignment output to obtain paths, and an unclosed bash fence could ship undetected.

How it was fixed

Removed the deprecated search toggle without adding --search; added Codex/agents global resolution and executable-file validation; added strict scalar path lookup and updated the generated /codex skill; closed the bad fence and added bounded nested syntax coverage. Release/version files are untouched.

Live evidence

• Corrected search run: gbrain, Actionbook, and zotero-arxiv-daily changed 23 -> 0; Cal.com and Plane remained 0 -> 0 controls. Identical-command gate PASS.
• Resolver/path run: LACP, gstack-auto, and Actionbook changed 1 -> 0; Cal.com and Stagehand remained 0 -> 0 controls. Identical-command gate PASS.
• Authenticated Codex review, challenge, and consult probes all used web search successfully with no search flag and confirmed cached-default / --search-means-live semantics.

Secondary verification

• bun run build — PASS (existing generated ship-skill token-ceiling warnings only)
• 483 targeted tests — PASS
• git diff --check — PASS

Full local review accounting and dossiers remain intentionally uncommitted under .review/wave-codex-model/.