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/api/cases.ts

@@ -0,0 +1,54 @@
+/**
+ * Cases domain hooks.
+ *
+ * Note on types: the FastAPI `/api/cases` endpoint doesn't declare a response
+ * model, so openapi-typescript emits `unknown` for its payload. Until the
+ * backend is annotated (see out-of-scope in the rewrite plan), we maintain a
+ * small local type that matches what the running API returns today. Any drift
+ * surfaces as a runtime TypeScript error the first time a property is touched.
+ */
+
+import { useQuery } from "@tanstack/react-query";
+import { apiRequest } from "./client";
+
+export type CaseStatus =
+  | "new"
+  | "uploading"
+  | "processing"
+  | "documents_ready"
+  | "outcome_set"
+  | "brainstorming"
+  | "direction_approved"
+  | "drafting"
+  | "qa_review"
+  | "drafted"
+  | "exported"
+  | "reviewed"
+  | "final";
+
+export type Case = {
+  case_number: string;
+  title: string;
+  status: CaseStatus;
+  subject?: string | null;
+  expected_outcome?: string | null;
+  created_at?: string;
+  updated_at?: string;
+};
+
+export const casesKeys = {
+  all: ["cases"] as const,
+  list: (detail: boolean) => [...casesKeys.all, "list", { detail }] as const,
+  detail: (caseNumber: string) =>
+    [...casesKeys.all, "detail", caseNumber] as const,
+};
+
+export function useCases(detail = false) {
+  return useQuery({
+    queryKey: casesKeys.list(detail),
+    queryFn: ({ signal }) =>
+      apiRequest<Case[]>(`/api/cases${detail ? "?detail=true" : ""}`, {
+        signal,
+      }),
+  });
+}