fix(codex): a CLI that cannot execute no longer reports CODEX_MODE: ready

Follow-up to #2477. The model probe it added does a real round trip, but its
final branch is the `else` of a "model 400" grep, so it swallowed spawn ENOENT,
non-executable binaries and missing vendor payloads alongside genuine network
timeouts. All three are deterministic — retrying never helps — yet they landed
in the fail-open bucket and resolved to `ready`, so every Codex pass was
skipped in silence and the review reported itself complete.

Observed live: @openai/codex was on PATH with an empty
vendor/aarch64-apple-darwin/codex/ directory. gstack said `ready` for two
months while no Codex pass ran.

Three changes:

- `_gstack_codex_model_probe` classifies deterministic install failures (exit
  126/127, or stderr matching ENOENT/ENOEXEC/EACCES/"cannot execute binary
  file") as MODEL_UNUSABLE_INSTALL, exit 2, never cached — a reinstall is
  picked up on the next probe. Exit 124 and genuine transients still fail open,
  which is what #2477 intended.

- The preflight chain captures the probe's code instead of testing it for
  truthiness, so exit 2 routes to a new `broken_install` mode whose remedy is
  `npm install -g @openai/codex` rather than "check your model pin". A missing
  binary and an unusable model are different problems with different fixes.

- `_gstack_codex_version_check` no longer reads a broken CLI as healthy. It ran
  `codex --version 2>/dev/null | head -1`, which captures head's status, not
  codex's — and 2>/dev/null discarded the one diagnostic available. It now
  captures the real exit code and warns on non-zero. Empty-but-successful
  output stays silent, per the existing "empty output → OK" case.

Tests: 6 added to test/codex-hardening.test.ts covering both broken-install
shapes, the exit-2 contract, no caching, the transient still failing open, the
model 400 still classifying as MODEL_UNUSABLE, and the version-check warning.
845 pass / 0 fail across all 8 suites touching the changed files.

Closes #2742

Wave-amended: autoplan hand-maintained preflight chain completed (tmpl+render); install-signature grep gated on failed spawn only; goldens regenerated against the wave tree (author's golden commit 5797d326 superseded); +2 tests

ship/sections/adversarial.md

@@ -35,10 +35,17 @@ elif ! command -v codex >/dev/null 2>&1; then
   _CODEX_MODE="not_installed"; _gstack_codex_log_event "codex_cli_missing" 2>/dev/null || true
 elif ! _gstack_codex_auth_probe >/dev/null 2>&1; then
   _CODEX_MODE="not_authed"; _gstack_codex_log_event "codex_auth_failed" 2>/dev/null || true
-elif ! _gstack_codex_model_probe; then
-  _CODEX_MODE="model_unusable"
 else
-  _CODEX_MODE="ready"; _gstack_codex_version_check 2>/dev/null || true
+  # Capture the probe's code: 2 means the CLI cannot execute at all, which is a
+  # different problem (and a different fix) from a model the account can't use.
+  _gstack_codex_model_probe; _CODEX_MP=$?
+  if [ "$_CODEX_MP" -eq 2 ]; then
+    _CODEX_MODE="broken_install"
+  elif [ "$_CODEX_MP" -ne 0 ]; then
+    _CODEX_MODE="model_unusable"
+  else
+    _CODEX_MODE="ready"; _gstack_codex_version_check 2>/dev/null || true
+  fi
 fi
 echo "CODEX_MODE: $_CODEX_MODE"
 ```
@@ -48,6 +55,7 @@ Branch on the echoed `CODEX_MODE`:
 - **`not_installed`** — Codex CLI absent. Print: "Codex not installed — using Claude subagent. Install for cross-model coverage: `npm install -g @openai/codex`." Fall back to the Claude subagent path.
 - **`under_codex`** — this session is already running INSIDE a Codex host, so spawning codex again is the same model reviewing itself at multiplied token cost (#2519). Print exactly one line: "[running under Codex — nested codex passes skipped; set GSTACK_FORCE_CODEX_REVIEW=1 to force]" and skip the codex invocations below; run the section's free in-host pass instead if it defines one.
 - **`not_authed`** — installed but no credentials. Print: "Codex installed but not authenticated — using Claude subagent. Run `codex login` or set `$CODEX_API_KEY`." Fall back to the Claude subagent path.
+- **`broken_install`** — the CLI is on PATH but cannot execute (spawn ENOENT, non-executable binary, missing vendor payload). Print: "Codex is installed but its binary cannot run — Codex passes skipped. Reinstall: `npm install -g @openai/codex`." Relay the probe's HINT lines and fall back to the Claude subagent path. This state exists because a missing binary used to land in the model probe's fail-open bucket and report `ready`, so every Codex pass was skipped silently (#2742).
 - **`model_unusable`** — authed but the account cannot use its configured model (#2477: HTTP 400 on every call, usually a stale `model =` pin in `~/.codex/config.toml`). Relay the probe's HINT lines, tell the user the one-line fix (update the pin; `[notice.model_migrations]` names the replacement), and fall back to the Claude subagent path. The ~10s round trip is cached for 1h; timeouts fail open to `ready`.
 - **`ready`** — run the Codex pass below.