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>

eslint.config.mjs

@@ -0,0 +1,18 @@
+import { defineConfig, globalIgnores } from "eslint/config";
+import nextVitals from "eslint-config-next/core-web-vitals";
+import nextTs from "eslint-config-next/typescript";
+
+const eslintConfig = defineConfig([
+  ...nextVitals,
+  ...nextTs,
+  // Override default ignores of eslint-config-next.
+  globalIgnores([
+    // Default ignores of eslint-config-next:
+    ".next/**",
+    "out/**",
+    "build/**",
+    "next-env.d.ts",
+  ]),
+]);
+
+export default eslintConfig;