feat(web): frontend foundation — Tailwind terminal theme, Query, Router, Zustand + live booth screen

Add tailwindcss (Bloomberg-terminal theme in index.css), @tanstack/react-query +
react-router, zustand, and Radix primitives. Router with role-guarded routes;
QueryClient wrapping the existing apiFetch; a small Zustand live store fed by a
/api/ws client that invalidates Query caches. Booth screen: live occupancy gauge
+ streaming entry/exit/payment feed. Vite proxies the WS upgrade.

Note: BoothScreen references the pay/exit modal + active-sessions panel added in
following commits; final HEAD builds.

apps/web/src/lib/query.ts

@@ -0,0 +1,28 @@
+import { QueryClient } from "@tanstack/react-query";
+
+// Single QueryClient for the app. TanStack Query owns SERVER state (fetch, cache,
+// refetch, loading/error) — wrapping the existing thin api.ts fetchers. Client/UI
+// state (live feed, WS status) lives in Zustand, not here. The WS layer invalidates
+// these caches on live events so Query stays the source of truth for server data.
+//
+// Defaults tuned for a single-appliance booth: no window-focus refetch (it's a
+// kiosk, not a tab someone switches to), and a short staleTime since the WS is the
+// real freshness mechanism — queries are the fallback/initial load.
+export const queryClient = new QueryClient({
+  defaultOptions: {
+    queries: {
+      refetchOnWindowFocus: false,
+      staleTime: 5_000,
+      retry: 1,
+    },
+  },
+});
+
+/** Stable query keys — referenced by both the screens and the WS invalidator. */
+export const qk = {
+  me: ["me"] as const,
+  occupancy: ["occupancy"] as const,
+  events: ["events"] as const,
+  activeSessions: ["active-sessions"] as const,
+  siteConfig: ["site-config"] as const,
+} as const;