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/src/transport/remote_control/tests.rs

@@ -96,6 +96,7 @@ fn remote_control_auth_dot_json(account_id: Option<&str>) -> AuthDotJson {
             account_id: account_id.map(str::to_string),
         }),
         last_refresh: Some(chrono::Utc::now()),
+        agent_identity: None,
     }
 }
 

codex-rs/app-server/src/transport/remote_control/websocket.rs

@@ -971,6 +971,7 @@ mod tests {
                 account_id: Some("account_id".to_string()),
             }),
             last_refresh: Some(Utc::now()),
+            agent_identity: None,
         }
     }