Phase 2: API client, typed hooks, live probe

- Add api:types script (openapi-typescript against live FastAPI)
- Generate src/lib/api/types.ts (2972 lines, 55 paths, 16 schemas)
- lib/api/client.ts: typed apiRequest + ApiError + makeQueryClient
  (staleTime 5s, no refetchOnWindowFocus to preserve editor state)
- lib/providers.tsx: QueryClientProvider client component, useState
  singleton so App Router re-renders don't dump the cache
- lib/api/cases.ts: Case type + casesKeys + useCases hook (pragmatic
  hand-typed Case pending backend response-model annotations)
- layout.tsx: wrap children with <Providers>
- Smoke test: CasesLiveProbe component on home page hitting live FastAPI
  via /api/cases rewrite proxy

Phase 2 deliverable check: useCases() returns typed Case[] from the
production FastAPI through the Next.js proxy. End-to-end wiring proven.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

web-ui/src/lib/providers.tsx

@@ -0,0 +1,17 @@
+"use client";
+
+import { useState, type ReactNode } from "react";
+import { QueryClientProvider } from "@tanstack/react-query";
+import { makeQueryClient } from "@/lib/api/client";
+
+/**
+ * Client-side providers. Creates ONE QueryClient instance per browser session
+ * via useState — Next.js App Router recreates the function on every render,
+ * so a naive `const client = makeQueryClient()` would dump the cache each time.
+ */
+export function Providers({ children }: { children: ReactNode }) {
+  const [queryClient] = useState(() => makeQueryClient());
+  return (
+    <QueryClientProvider client={queryClient}>{children}</QueryClientProvider>
+  );
+}