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>

tsconfig.json

@@ -1,32 +1,34 @@
-/* To learn more about this file see: https://angular.io/config/tsconfig. */
 {
-  "compileOnSave": false,
   "compilerOptions": {
-    "baseUrl": "./",
-    "outDir": "./dist/out-tsc",
-    "forceConsistentCasingInFileNames": true,
+    "target": "ES2017",
+    "lib": ["dom", "dom.iterable", "esnext"],
+    "allowJs": true,
+    "skipLibCheck": true,
     "strict": true,
-    "noImplicitOverride": true,
-    "noPropertyAccessFromIndexSignature": true,
-    "noImplicitReturns": true,
-    "noFallthroughCasesInSwitch": true,
-    "sourceMap": true,
-    "declaration": false,
-    "downlevelIteration": true,
-    "experimentalDecorators": true,
-    "moduleResolution": "node",
-    "importHelpers": true,
-    "target": "es2020",
-    "module": "es2020",
-    "lib": [
-      "es2020",
-      "dom"
-    ]
+    "noEmit": true,
+    "esModuleInterop": true,
+    "module": "esnext",
+    "moduleResolution": "bundler",
+    "resolveJsonModule": true,
+    "isolatedModules": true,
+    "jsx": "react-jsx",
+    "incremental": true,
+    "plugins": [
+      {
+        "name": "next"
+      }
+    ],
+    "paths": {
+      "@/*": ["./*"]
+    }
   },
-  "angularCompilerOptions": {
-    "enableI18nLegacyMessageIdFormat": false,
-    "strictInjectionParameters": true,
-    "strictInputAccessModifiers": true,
-    "strictTemplates": true
-  }
+  "include": [
+    "next-env.d.ts",
+    "**/*.ts",
+    "**/*.tsx",
+    ".next/types/**/*.ts",
+    ".next/dev/types/**/*.ts",
+    "**/*.mts"
+  ],
+  "exclude": ["node_modules"]
 }