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

bun.lock

@@ -266,6 +266,7 @@
         "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",
       },
@@ -3134,6 +3135,8 @@
 
     "wrappy": ["wrappy@1.0.2", "", {}, "sha512-l4Sp/DRseor9wL6EvV2+TuQn63dMkPjZ/sp9XkghTEbV9KlPS1xUsZ3u7/IQO4wxtcFB4bgpQPRcR3QCvezPcQ=="],
 
+    "ws": ["ws@8.19.0", "", { "peerDependencies": { "bufferutil": "^4.0.1", "utf-8-validate": ">=5.0.2" }, "optionalPeers": ["bufferutil", "utf-8-validate"] }, "sha512-blAT2mjOEIi0ZzruJfIhb3nps74PRWTCz1IjglWEEpQl5XS/UNama6u2/rjFkDDouqr4L67ry+1aGIALViWjDg=="],
+
     "wsl-utils": ["wsl-utils@0.1.0", "", { "dependencies": { "is-wsl": "^3.1.0" } }, "sha512-h3Fbisa2nKGPxCpm89Hk33lBLsnaGBvctQopaBSOW/uIs6FTe1ATyAnKFJrzVs9vpGdsTe73WF3V4lIsk4Gacw=="],
 
     "xml2js": ["xml2js@0.5.0", "", { "dependencies": { "sax": ">=0.6.0", "xmlbuilder": "~11.0.0" } }, "sha512-drPFnkQJik/O+uPKpqSgr22mpuFHqKdbS835iAQrUC73L2F5WkboIRd63ai/2Yg6I1jzifPFKH2NTK+cfglkIA=="],