feat(web): add WebSocket client and context infrastructure

- WsClient class: connect/disconnect/send/on/off/isConnected/clearCallbacks
- connect() derives wss:// from https:// automatically, returns Promise<void>
- on/off typed with Extract<WsServerMessage, { type: T }> for precise
  callback narrowing, callbacks stored as Map<string, Set<fn>>
- ws-context.ts: WsContextValue type + WsContext definition
- ws-provider.tsx: WsProvider with module-level wsClient singleton,
  owns connection lifecycle (connect/disconnect/isConnected state)
- ws-hooks.ts: useWsClient, useWsConnected, useWsConnect, useWsDisconnect

apps/web/src/lib/ws-provider.tsx

@@ -0,0 +1,44 @@
+import { useCallback, useEffect, useState } from "react";
+import type { ReactNode } from "react";
+import { WsClient } from "./ws-client.js";
+import { WsContext } from "./ws-context.js";
+
+const wsClient = new WsClient();
+
+export const WsProvider = ({ children }: { children: ReactNode }) => {
+  const [isConnected, setIsConnected] = useState(false);
+
+  const connect = useCallback(async (url: string): Promise<void> => {
+    wsClient.onClose = () => setIsConnected(false);
+    wsClient.onError = () => setIsConnected(false);
+    try {
+      await wsClient.connect(url);
+      setIsConnected(true);
+    } catch (err) {
+      setIsConnected(false);
+      throw err;
+    }
+  }, []);
+
+  const disconnect = useCallback((): void => {
+    wsClient.disconnect();
+    setIsConnected(false);
+  }, []);
+
+  useEffect(() => {
+    return () => {
+      wsClient.disconnect();
+      wsClient.clearCallbacks();
+      wsClient.onClose = null;
+      wsClient.onError = null;
+    };
+  }, []);
+
+  return (
+    <WsContext.Provider
+      value={{ client: wsClient, isConnected, connect, disconnect }}
+    >
+      {children}
+    </WsContext.Provider>
+  );
+};