Add frontend API client and TanStack Query hooks

Install @tanstack/react-query, create a fetch-based API client with typed
functions for all endpoints, and add query/mutation hooks for games, pokemon,
runs, and encounters. Includes Vite dev proxy for /api and QueryClientProvider
setup.

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

frontend/src/api/client.ts

@@ -0,0 +1,51 @@
+const API_BASE = import.meta.env.VITE_API_URL ?? ''
+
+export class ApiError extends Error {
+  status: number
+
+  constructor(status: number, message: string) {
+    super(message)
+    this.name = 'ApiError'
+    this.status = status
+  }
+}
+
+async function request<T>(
+  path: string,
+  options?: RequestInit,
+): Promise<T> {
+  const res = await fetch(`${API_BASE}/api/v1${path}`, {
+    ...options,
+    headers: {
+      'Content-Type': 'application/json',
+      ...options?.headers,
+    },
+  })
+
+  if (!res.ok) {
+    const body = await res.json().catch(() => ({}))
+    throw new ApiError(res.status, body.detail ?? res.statusText)
+  }
+
+  if (res.status === 204) return undefined as T
+  return res.json()
+}
+
+export const api = {
+  get: <T>(path: string) => request<T>(path),
+
+  post: <T>(path: string, body: unknown) =>
+    request<T>(path, {
+      method: 'POST',
+      body: JSON.stringify(body),
+    }),
+
+  patch: <T>(path: string, body: unknown) =>
+    request<T>(path, {
+      method: 'PATCH',
+      body: JSON.stringify(body),
+    }),
+
+  del: <T = void>(path: string) =>
+    request<T>(path, { method: 'DELETE' }),
+}