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>

vitest.config.mts

@@ -0,0 +1,26 @@
+import { fileURLToPath } from "node:url";
+import { defineConfig } from "vitest/config";
+
+// Unit tests cover the pure logic in lib/ only (docs/rewrite-plan.md, Q10), so
+// a plain Node environment is enough - no DOM, no React.
+//
+// TZ is pinned to somewhere that is *not* Europe/Berlin on purpose: the date
+// code must produce Berlin wall times regardless of the machine it runs on,
+// and a test run in Berlin would hide exactly that class of bug.
+export default defineConfig({
+  test: {
+    environment: "node",
+    include: ["**/*.test.ts"],
+    exclude: ["node_modules/**", ".next/**"],
+    passWithNoTests: true,
+    env: {
+      TZ: "America/New_York",
+      // lib/env.ts throws without these; the values are never contacted - api.test.ts stubs fetch.
+      NEXT_PUBLIC_API_BASE_URL: "https://api.test",
+      NEXT_PUBLIC_ADMIN_APP_URL: "https://admin.test",
+    },
+  },
+  resolve: {
+    alias: { "@": fileURLToPath(new URL(".", import.meta.url)) },
+  },
+});