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/core/src/lib.rs

@@ -5,6 +5,7 @@
 // the TUI or the tracing stack).
 #![deny(clippy::print_stdout, clippy::print_stderr)]
 
+mod agent_identity;
 mod apply_patch;
 mod apps;
 mod arc_monitor;