feat(terminal): add persistent websocket transport for low-latency input (#348)

* fix(server): resolve terminal WebSocket proxy conflict and implement server-side transport

- Disables proxy websocket handling conflict in server proxy config to fix 1006 abnormal closes.
- Implements server-side WebSocket upgrade and connection handling for terminal input.
- Adds server-side debug instrumentation for WS lifecycle events.
- Includes terminal input WS protocol definition and unit tests.

* feat(ui): implement hardened terminal WebSocket transport with idempotency and diagnostics

- Adds client-side WebSocket transport manager with automatic reconnection and jitter.
- Implements idempotency and debug instrumentation for terminal input WS.
- Adds HMR dispose cleanup for terminal WS transport manager.
- Primes terminal input transport when terminal view becomes active.
- Updates terminal session types to include input capabilities.

* refactor(terminal): remove temporary websocket debug instrumentation

packages/web/package.json

@@ -60,6 +60,7 @@
     "strip-json-comments": "^5.0.3",
     "tailwind-merge": "^3.3.1",
     "web-push": "^3.6.7",
+    "ws": "^8.18.3",
     "yaml": "^2.8.1",
     "zustand": "^5.0.8"
   },