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/components/cases/cases-live-probe.tsx

@@ -0,0 +1,51 @@
+"use client";
+
+import { useCases } from "@/lib/api/cases";
+
+/**
+ * Phase 2 smoke-test component — proves that the typed API client, the
+ * TanStack Query provider, the Next.js rewrite proxy, and the FastAPI backend
+ * are all wired up correctly end-to-end. Temporary; replaced in Phase 3 by the
+ * real case list view.
+ */
+export function CasesLiveProbe() {
+  const { data, isLoading, isError, error } = useCases();
+
+  if (isLoading) {
+    return (
+      <p className="text-ink-muted">טוען תיקים מה-API…</p>
+    );
+  }
+
+  if (isError) {
+    return (
+      <div className="text-danger">
+        <p className="font-medium">שגיאה בטעינת תיקים</p>
+        <p className="text-sm text-ink-muted">
+          {error instanceof Error ? error.message : "שגיאה לא ידועה"}
+        </p>
+      </div>
+    );
+  }
+
+  const count = data?.length ?? 0;
+
+  return (
+    <div className="space-y-2">
+      <p className="text-ink">
+        <span className="font-semibold text-navy">{count}</span>{" "}
+        תיקים טעונים מה-API בהצלחה.
+      </p>
+      {data && data.length > 0 && (
+        <ul className="text-sm text-ink-muted space-y-1">
+          {data.slice(0, 3).map((c) => (
+            <li key={c.case_number}>
+              <span className="text-gold-deep">{c.case_number}</span> — {c.title}
+            </li>
+          ))}
+          {data.length > 3 && <li>ועוד {data.length - 3}…</li>}
+        </ul>
+      )}
+    </div>
+  );
+}