Register agent identities behind use_agent_identity (#17386)

## Summary

Stack PR 2 of 4 for feature-gated agent identity support.

This PR adds agent identity registration behind
`features.use_agent_identity`. It keeps the app-server protocol
unchanged and starts registration after ChatGPT auth exists rather than
requiring a client restart.

## Stack

- PR1: https://github.com/openai/codex/pull/17385 - add
`features.use_agent_identity`
- PR2: https://github.com/openai/codex/pull/17386 - this PR
- PR3: https://github.com/openai/codex/pull/17387 - register agent tasks
when enabled
- PR4: https://github.com/openai/codex/pull/17388 - use `AgentAssertion`
downstream when enabled

## Validation

Covered as part of the local stack validation pass:

- `just fmt`
- `cargo test -p codex-core --lib agent_identity`
- `cargo test -p codex-core --lib agent_assertion`
- `cargo test -p codex-core --lib websocket_agent_task`
- `cargo test -p codex-api api_bridge`
- `cargo build -p codex-cli --bin codex`

## Notes

The full local app-server E2E path is still being debugged after PR
creation. The current branch stack is directionally ready for review
while that follow-up continues.

codex-rs/app-server/tests/common/auth_fixtures.rs

@@ -163,6 +163,7 @@ pub fn write_chatgpt_auth(
         openai_api_key: None,
         tokens: Some(tokens),
         last_refresh,
+        agent_identity: None,
     };
 
     save_auth(codex_home, &auth, cli_auth_credentials_store_mode).context("write auth.json")

codex-rs/app-server/tests/suite/v2/app_list.rs

@@ -117,6 +117,7 @@ async fn list_apps_returns_empty_with_api_key_auth() -> Result<()> {
             openai_api_key: Some("test-api-key".to_string()),
             tokens: None,
             last_refresh: None,
+            agent_identity: None,
         },
         AuthCredentialsStoreMode::File,
     )?;