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>

lib/api-errors.ts

@@ -0,0 +1,31 @@
+import { ApiError } from "@/lib/api";
+
+/**
+ * What to tell an editor when a call fails. German, one sentence, no status
+ * codes up front - the code is appended for anything unexpected, so a
+ * screenshot of the message is still useful to whoever debugs it.
+ *
+ * 401 is listed for completeness; callers should send the user to the login
+ * page instead of showing it (see `isSessionExpired`).
+ */
+export const describeApiError = (error: unknown): string => {
+  if (!(error instanceof ApiError)) {
+    return "Unerwarteter Fehler. Bitte versuche es erneut.";
+  }
+  switch (error.status) {
+    case 0:
+      return "Keine Verbindung zum Server. Bitte prüfe deine Internetverbindung.";
+    case 401:
+      return "Deine Sitzung ist abgelaufen.";
+    case 403:
+      return "Dein Konto hat keine Berechtigung (mehr) für den Kalender.";
+    case 200:
+      // A 200 that the client decided was a failure (e.g. "0 rows were updated") carries its own German message.
+      return error.message;
+    default:
+      return `Der Server hat einen Fehler gemeldet (${error.status}). Bitte versuche es erneut.`;
+  }
+};
+
+/** Nobody is signed in any more - the one case worth a trip to the login page. */
+export const isSessionExpired = (error: unknown): boolean => error instanceof ApiError && error.status === 401;