fix(app-server): SpawnedCodexAppServerClient.initialize is unbounded (same hang class as #29) #31

Problem

BrokerCodexAppServerClient.initialize got bounded handshake timeouts in #30 (connect 2s + initialize 5s, EBROKERTIMEOUT → direct fallback). Its sibling SpawnedCodexAppServerClient.initialize has the same unbounded shape and was left out of scope there.

plugins/codex/scripts/lib/app-server.mjs:

```js
// SpawnedCodexAppServerClient.initialize — no deadline
await this.request("initialize", {
clientInfo: this.options.clientInfo ?? DEFAULT_CLIENT_INFO,
capabilities: this.options.capabilities ?? DEFAULT_CAPABILITIES
});
```

If a spawned codex app-server child accepts stdin and then stalls before answering initialize (slow auth check, cold model-provider bootstrap, Windows PATH stall), the client hangs forever — the same failure class #30 closed on the broker path, just on the direct path.

This also weakens the #30 fallback: when withAppServer retries direct after a broker-handshake timeout, the retry itself has no initialize deadline.

Proposed fix (deeper than #30)

Put an optional timeoutMs on AppServerClientBase.request() (default undefined — no deadline, backward compatible), wired from both initialize() overrides and from captureTurn's startRequest. Then:

• BrokerCodexAppServerClient.initialize drops its inline Promise.race (~40 lines) and calls this.request(\"initialize\", {...}, { timeoutMs }).
• SpawnedCodexAppServerClient.initialize gets the bound for free.
• The withAppServer OR-chain (BROKER_BUSY_RPC_CODE || EBROKERTIMEOUT || ENOENT || ECONNREFUSED) collapses to a single broker-transport-error predicate by tagging broker-fatal errors at their source.

TDD

Reproduce first: drive SpawnedCodexAppServerClient.initialize against a fake codex app-server that accepts stdin but never answers initialize, race against a watchdog → today it hangs. Then bound it.

Context

• Spun out of Codex adversarial review of fix(broker): bound broker handshake so a wedged broker can't hang the client (closes #29) #30 (cycle 1) — the reviewer flagged the spawned twin as the same hang class.
• Not a blocker for fix: broker-busy hang — second /codex:* task waits forever for shared broker (openai#509) #29/fix(broker): bound broker handshake so a wedged broker can't hang the client (closes #29) #30 (the reported bug was the broker path); this is the latent sibling.

Refs #29, #30, openai#509.