Rewrite the calendar frontend in Next.js

Replaces the Angular 18 app with Next.js 16 / React 19 / Tailwind 4 / shadcn,
the same stack and design system as nachklang-feedback, planned in
docs/rewrite-plan.md.

- Admin: all calendars in one mobile-friendly list (month groups, calendar
  chips, Kommend/Vergangen/Alle, search, sort, filters in the URL), an edit
  sheet for create/edit/duplicate/delete, publish confirmation, and an
  "Abonnieren" dialog with subscription links for every calendar.
- Public landing page: subscribe links from env instead of hardcoded, plus
  the next public events, server-rendered and revalidated every 5 minutes.
- All times handled explicitly as Europe/Berlin; whole-day events stored as
  00:00-23:59. Fixes carried over from the Angular app: the move dialog
  leaking a cancelled calendar change, saves that looked saved when they
  failed, in-place Date mutation, and duplicated calendar-id mappings.
- Same shared-session auth as before (proxy.ts gate, /admin/me, 401 vs 403).
- 112 Vitest tests over lib/; docs in docs/ (architecture, features,
  gotchas, API wish list, deployment).

Needs the API branch feature/calendar-ical-escaping-subscriptions deployed
first (GET /calendar/events/subscriptions).

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

app/layout.tsx

@@ -0,0 +1,35 @@
+import type { Metadata, Viewport } from "next";
+import { Inter } from "next/font/google";
+import "./globals.css";
+import { cn } from "@/lib/utils";
+
+// Same design system as nachklang-feedback: shadcn preset b7ClO5que (style:
+// luma, base: mist, theme: indigo, font: inter). next/font self-hosts the font
+// at build time, so there is no runtime Google Fonts call.
+const inter = Inter({ subsets: ["latin"], variable: "--font-sans" });
+
+export const metadata: Metadata = {
+  title: "Nachklang e.V. – Kalender",
+  description: "Veranstaltungskalender von Nachklang e.V.",
+};
+
+export const viewport: Viewport = {
+  width: "device-width",
+  initialScale: 1,
+  viewportFit: "cover",
+};
+
+export default function RootLayout({
+  children,
+}: Readonly<{
+  children: React.ReactNode;
+}>) {
+  return (
+    <html
+      lang="de"
+      className={cn("h-full", "antialiased", "font-sans", inter.variable)}
+    >
+      <body className="min-h-full flex flex-col">{children}</body>
+    </html>
+  );
+}