feat: add explicit AgentIdentity auth mode (#18785)

## Summary

This PR adds `CodexAuth::AgentIdentity` as an explicit auth mode.

An AgentIdentity auth record is a standalone `auth.json` mode. When
`AuthManager::auth().await` loads that mode, it registers one
process-scoped task and stores it in runtime-only state on the auth
value. Header creation stays synchronous after that because the task is
initialized before callers receive the auth object.

This PR also removes the old feature flag path. AgentIdentity is
selected by explicit auth mode, not by a hidden flag or lazy mutation of
ChatGPT auth records.

Reference old stack: https://github.com/openai/codex/pull/17387/changes

## Design Decisions

- AgentIdentity is a real auth enum variant because it can be the only
credential in `auth.json`.
- The process task is ephemeral runtime state. It is not serialized and
is not stored in rollout/session data.
- Account/user metadata needed by existing Codex backend checks lives on
the AgentIdentity record for now.
- `is_chatgpt_auth()` remains token-specific.
- `uses_codex_backend()` is the broader predicate for ChatGPT-token auth
and AgentIdentity auth.

## Stack

1. https://github.com/openai/codex/pull/18757: full revert
2. https://github.com/openai/codex/pull/18871: isolated Agent Identity
crate
3. This PR: explicit AgentIdentity auth mode and startup task allocation
4. https://github.com/openai/codex/pull/18811: migrate Codex backend
auth callsites through AuthProvider
5. https://github.com/openai/codex/pull/18904: accept AgentIdentity JWTs
and load `CODEX_AGENT_IDENTITY`

## Testing

Tests: targeted Rust checks, cargo-shear, Bazel lock check, and CI.

codex-rs/app-server-protocol/schema/json/ServerNotification.json

@@ -436,6 +436,13 @@
             "chatgptAuthTokens"
           ],
           "type": "string"
+        },
+        {
+          "description": "Programmatic Codex auth backed by a registered Agent Identity.",
+          "enum": [
+            "agentIdentity"
+          ],
+          "type": "string"
         }
       ]
     },