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>

setup-gbrain/SKILL.md

@@ -778,7 +778,9 @@ Capture the JSON output. It contains: `gbrain_on_path`, `gbrain_version`,
 `gbrain_config_exists`, `gbrain_engine`, `gbrain_doctor_ok`, `gbrain_mcp_mode`,
 `gstack_brain_sync_mode`, `gstack_brain_git`, `gstack_artifacts_remote`, and
 the v1.34.0.0+ `gbrain_local_status` field (one of: `ok`, `no-cli`,
-`missing-config`, `broken-config`, `broken-db`).
+`missing-config`, `broken-config`, `broken-db`, `timeout`). Treat `timeout`
+like `ok` (slow-but-healthy engine, #1964) — it never triggers Step 1.5
+remediation.
 
 Skip downstream steps that are already done. Report the detected state in
 one line so the user knows what you found:

setup-gbrain/SKILL.md.tmpl

@@ -66,7 +66,9 @@ Capture the JSON output. It contains: `gbrain_on_path`, `gbrain_version`,
 `gbrain_config_exists`, `gbrain_engine`, `gbrain_doctor_ok`, `gbrain_mcp_mode`,
 `gstack_brain_sync_mode`, `gstack_brain_git`, `gstack_artifacts_remote`, and
 the v1.34.0.0+ `gbrain_local_status` field (one of: `ok`, `no-cli`,
-`missing-config`, `broken-config`, `broken-db`).
+`missing-config`, `broken-config`, `broken-db`, `timeout`). Treat `timeout`
+like `ok` (slow-but-healthy engine, #1964) — it never triggers Step 1.5
+remediation.
 
 Skip downstream steps that are already done. Report the detected state in
 one line so the user knows what you found: