fix(gbrain): classify probe timeout as its own status; sync proceeds instead of skipping (#1964)

The 5s engine probe misclassified healthy-but-slow engines (cold Supabase
pooler connections measured at 6.9-10.7s) as broken-config, so /sync-gbrain
silently skipped code+memory and told the user their config was malformed.

- New "timeout" status: probe killed at the deadline with no recognized
  stderr pattern. Default deadline is now 15s, overridable via
  GSTACK_GBRAIN_PROBE_TIMEOUT_MS (tests set 300ms against a fake that
  sleeps 2s).
- Sync stages PROCEED on timeout with a stderr warning naming the env knob;
  a genuinely-dead engine surfaces its real error at the first operation
  instead of a false config diagnosis.
- Consistency everywhere "ok" gated behavior: gstack-gbrain-detect --is-ok
  exits 0 on timeout, and gen-skill-docs' detection gate accepts it, so a
  slow engine no longer silently suppresses brain-aware features.
- Status cache: key now includes the effective probe timeout (raising it
  invalidates a cached timeout) and GBRAIN_HOME; config detection honors
  GBRAIN_HOME so relocated-home users stop being misclassified as
  missing-config.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

test/gbrain-sync-skip.test.ts

@@ -42,7 +42,7 @@ interface FakeEnv {
  */
 function makeEnv(opts: {
   withGbrain: boolean;
-  gbrainBehavior?: "ok" | "broken-db" | "broken-config";
+  gbrainBehavior?: "ok" | "broken-db" | "broken-config" | "slow";
   withConfig: boolean;
 }): FakeEnv {
   const tmp = mkdtempSync(join(tmpdir(), "gbrain-sync-skip-"));
@@ -65,19 +65,26 @@ function makeEnv(opts: {
 
   if (opts.withGbrain) {
     const behavior = opts.gbrainBehavior || "ok";
-    const stderrLine =
-      behavior === "broken-db"
-        ? 'echo "Cannot connect to database: . Fix: Check your connection URL in ~/.gbrain/config.json" >&2'
-        : behavior === "broken-config"
-          ? 'echo "Error: malformed config.json" >&2'
-          : "";
-    const exitCode = behavior === "ok" ? 0 : 1;
+    // "slow": healthy engine, cold pooler connection (#1964) — sleeps past the
+    // (test-lowered) probe timeout on `sources list`, then answers fine.
+    const sourcesBlock =
+      behavior === "slow"
+        ? `  sleep 2
+  echo '{"sources":[]}'
+  exit 0`
+        : behavior === "ok"
+          ? `  echo '{"sources":[]}'
+  exit 0`
+          : `  ${
+              behavior === "broken-db"
+                ? 'echo "Cannot connect to database: . Fix: Check your connection URL in ~/.gbrain/config.json" >&2'
+                : 'echo "Error: malformed config.json" >&2'
+            }
+  exit 1`;
     const fake = `#!/bin/sh
 if [ "$1" = "--version" ]; then echo "gbrain 0.33.1.0"; exit 0; fi
 if [ "$1 $2" = "sources list" ]; then
-  if [ ${exitCode} -eq 0 ]; then echo '{"sources":[]}'; exit 0; fi
-  ${stderrLine}
-  exit ${exitCode}
+${sourcesBlock}
 fi
 if [ "$1" = "--help" ]; then echo "  import"; exit 0; fi
 exit 0
@@ -95,7 +102,11 @@ exit 0
   };
 }
 
-function runOrchestrator(env: FakeEnv, args: string[]): { stdout: string; stderr: string; exitCode: number } {
+function runOrchestrator(
+  env: FakeEnv,
+  args: string[],
+  extraEnv: Record<string, string> = {},
+): { stdout: string; stderr: string; exitCode: number } {
   // Initialize a git repo in the sandbox so repoRoot() finds it (otherwise
   // code stage skips with "not in git repo" before our check ever fires).
   spawnSync("git", ["init", "-q", env.home], { encoding: "utf-8" });
@@ -113,6 +124,7 @@ function runOrchestrator(env: FakeEnv, args: string[]): { stdout: string; stderr
       HOME: env.home,
       GSTACK_HOME: env.gstackHome,
       PATH: `${env.bindir}:/usr/bin:/bin`,
+      ...extraEnv,
     },
   });
   return {
@@ -123,6 +135,23 @@ function runOrchestrator(env: FakeEnv, args: string[]): { stdout: string; stderr
 }
 
 describe("gstack-gbrain-sync — split-engine SKIP (plan D12)", () => {
+  it("PROCEEDS (with warning) when the engine probe times out — slow is not broken (#1964)", () => {
+    const env = makeEnv({ withGbrain: true, gbrainBehavior: "slow", withConfig: true });
+    try {
+      const r = runOrchestrator(env, ["--code-only"], {
+        GSTACK_GBRAIN_PROBE_TIMEOUT_MS: "300",
+      });
+      const out = r.stdout + r.stderr;
+      // The stage must NOT be skipped with the local-engine reason...
+      expect(out).not.toContain("local engine timeout");
+      expect(out).not.toContain("config.json is malformed");
+      // ...and the proceed-with-warning line must name the env knob.
+      expect(out).toContain("GSTACK_GBRAIN_PROBE_TIMEOUT_MS");
+    } finally {
+      env.cleanup();
+    }
+  }, 30_000); // proceeding runs the real code-import path against the slow fake (~11s)
+
   it("SKIPs code stage when local engine is broken-db; brain-sync still attempted", () => {
     const env = makeEnv({ withGbrain: true, gbrainBehavior: "broken-db", withConfig: true });
     try {