[codex] Fix desktop stale WebSocket prompt timeout

[Tamaz-sujashvili]

Fixes #40164.

Summary

• Close stale desktop JSON-RPC WebSockets when an RPC request times out.
• Reconnect using the gateway client's actual connection state.
• Treat a prompt.submit timeout as accepted when session.status confirms the backend turn is running.
• Rebind live TUI session transports to the current WebSocket on session-scoped requests.
• Add frontend and backend regression coverage.

Root Cause

After idle time, the desktop WebSocket could become stale. The backend accepted prompt.submit, but failed to send the response over the old socket, producing request timed out: prompt.submit in the renderer. Later sends hit the still-running backend and surfaced as session busy.

Validation

• npm --workspace apps/desktop run test:ui -- src/lib/json-rpc-gateway.test.ts
• npm --workspace apps/desktop run type-check
• scripts/run_tests.sh tests/test_tui_gateway_server.py -- -k session_lookup_rebinds_current_transport

[teknium1]

Thanks for targeting a real stale-transport failure mode. Current apps/shared/src/json-rpc-gateway.ts:267-273 still rejects a timed-out RPC without closing the socket, while apps/desktop/src/app/gateway/hooks/use-gateway-request.ts:104-116 only reconnects for disconnected/closed errors.

Problems

• The Desktop submit implementation moved after this branch: apps/desktop/src/app/session/hooks/use-prompt-actions.ts no longer exists on main. The active flow is apps/desktop/src/app/session/hooks/use-prompt-actions/submit.ts:337-381, which already has selected-session timeout recovery, and apps/desktop/src/hermes.ts:74-82, which gives prompt.submit a 1,800,000 ms timeout. The proposed status path needs to be integrated with that current behavior.
• apps/desktop/src/lib/json-rpc-gateway.test.ts proves socket closure only. It does not exercise the accepted-submit/lost-response/reconnect path or guard against duplicate submission.

Suggested changes

• Port the behavior to the current submit pipeline and add an end-to-end unit regression for that sequence.

Automated hermes-sweeper review.

[teknium1]

This submit hook was extracted on current main: the live path is now apps/desktop/src/app/session/hooks/use-prompt-actions/submit.ts:337-381, which already resumes and retries selected stored sessions after a timeout. Please port and reconcile this recovery there rather than applying the old-hook logic unchanged.

[100yenadmin]

The still-relevant Desktop heartbeat and reconnect-recovery behavior from this PR has been adapted to the current shared gateway architecture in #83166. Tamaz Sujashvili is credited in the combined PR and as a co-author on the synthesized integration commit. This cross-link does not close or rewrite this PR.