Reconnect Codex tmux proxy after app-server drops

[axeldelafosse]

Summary

• keep the Codex tmux proxy alive when its upstream app-server websocket drops
• reconnect the proxy upstream with capped backoff and reinitialize the upstream protocol state after reconnect
• add a live websocket regression test proving the TUI-side socket stays connected and can submit another turn after reconnect

Root cause

In paired tmux mode, tmux handoff releases the local Codex app-server handles. That leaves the tmux proxy as the only remaining supervisor for the Codex-side connection. The proxy previously treated any upstream websocket close as terminal and stopped immediately, which dropped the Codex TUI remote socket and left only a dead pane via remain-on-exit.

User impact

Paired tmux sessions no longer fail fast on a live app-server websocket drop. The proxy retries the upstream connection instead of immediately tearing down the TUI-side socket.

Validation

• bun test
• bun run fix
• bun run check

[gemini-code-assist]

Code Review

This pull request introduces automatic reconnection logic for the CodexTmuxProxy, featuring exponential backoff, a formal initialization handshake, and updated health check endpoints. These changes ensure that the proxy can recover from upstream disconnects without dropping existing TUI socket connections. Feedback was provided to improve the clarity of the error message returned while the proxy is attempting to reconnect to the app-server.

[gemini-code-assist]

The error message 'codex app-server is reconnecting' is slightly misleading because the proxy is the one reconnecting to the app-server. Consider changing this to 'codex app-server connection is being established' for better clarity.