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/ui/src/lib/api/types.ts

@@ -33,6 +33,17 @@ export interface TerminalSession {
   sessionId: string;
   cols: number;
   rows: number;
+  capabilities?: {
+    input?: {
+      preferred?: 'ws' | 'http';
+      transports?: Array<'ws' | 'http'>;
+      ws?: {
+        path: string;
+        v?: number;
+        enc?: string;
+      };
+    };
+  };
 }
 
 export interface TerminalStreamEvent {