[BUG] Bundled GrowthBook clientKey still returns 400 "Invalid API Key" on 2.1.266 — Remote Control fails closed (regression/reopen of #64151)

## Summary

Same bug as #64151 (closed by stale-bot without a fix), still present on **2.1.266** — much later than the versions originally reported (2.1.149 / 2.1.157 / 2.1.158). The bundled GrowthBook clientKey `sdk-zAZezfDKGoZuXXKe` (apiHost `https://cdn.growthbook.io`) is currently rejected by the CDN, so zero feature flags load and Remote Control fails closed with a misleading network-sounding error.

## Environment

- Claude Code **2.1.266**, macOS arm64
- `claude auth status`: `loggedIn: true`, `authMethod: claude.ai`, `apiProvider: firstParty`, `analyticsDisabled: false`, `subscriptionType: max`
- No telemetry/GrowthBook env vars set (`DISABLE_TELEMETRY`, `DISABLE_GROWTHBOOK`, `CLAUDE_CODE_DISABLE_NONESSENTIAL_TRAFFIC`, `DO_NOT_TRACK` all unset — verified via `env`)

## Repro (machine-independent, no auth required)

```
$ curl https://cdn.growthbook.io/api/features/sdk-zAZezfDKGoZuXXKe
{"status":400,"error":"Invalid API Key"}
```

Reproduced 5/5 consecutive attempts just now (2026-09-09). Confirmed `sdk-zAZezfDKGoZuXXKe` is still the hardcoded clientKey in the 2.1.266 binary via `strings`.

## `claude doctor` output

```
Remote Control
Couldn't verify Remote Control eligibility — the feature-flag service was unreachable (offline or blocked). Retry, or run with --debug / claude doctor for details.
- Remote Control availability could not be verified (no server response this session)
```

Failed consistently across 3 separate `claude doctor` runs, several minutes apart.

## Ruled out before filing

- Corporate proxy/VPN: confirmed both `api.anthropic.com` and `cdn.growthbook.io` return normal, unblocked responses through the network in question (valid TLS, correct HTTP status, expected JSON bodies) — this is a genuine upstream key rejection, not a network block.
- Env vars that are known to disable GrowthBook evaluation: confirmed absent.
- Stale/cached auth: `claude auth status` shows a valid, current claude.ai Max session.

## Impact

Remote Control (and presumably Channels, per #64151) silently unavailable. The error message ("feature-flag service was unreachable (offline or blocked)") reads as a local network problem, which sends users on a long, unproductive troubleshooting path (proxy/VPN checks, cert issues) before finding this is a server-side key problem — as happened here.

## Ask

1. Rotate/restore the GrowthBook clientKey so `cdn.growthbook.io` accepts it, and confirm the fix in this issue rather than letting it go stale again.
2. Since #64151 was auto-closed by inactivity without a fix or maintainer response, consider exempting confirmed-repro issues with a live `has repro` label from the stale-bot, or at minimum leave a closing comment when a real fix ships.

Related: #64151 (same key, same symptom, closed by staleness bot 2026-09-05 without resolution).

Reproduce the failure with the documented curl request, then compare the bundled sdk-zAZezfDKGoZuXXKe value in the 2.1.266 binary with the GrowthBook endpoint response. Check the claude doctor Remote Control result after the client key is accepted; done means feature flags load and Remote Control no longer reports the service as unreachable.

Written by the indexing model from the issue text.