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>

components/admin/CalendarBadge.tsx

@@ -0,0 +1,19 @@
+import { calendarById } from "@/lib/calendars";
+import { cn } from "@/lib/utils";
+
+/** The calendar an event belongs to, in that calendar's colour - never the bare id. */
+export function CalendarBadge({ calendarId, className }: { calendarId: number; className?: string }) {
+  const calendar = calendarById(calendarId);
+  return (
+    <span
+      className={cn(
+        "inline-flex h-5 items-center gap-1.5 rounded-full px-2 text-xs font-medium ring-1 ring-inset",
+        calendar?.badgeClass ?? "bg-muted text-muted-foreground ring-border",
+        className,
+      )}
+    >
+      <span aria-hidden className={cn("size-1.5 rounded-full", calendar?.dotClass ?? "bg-muted-foreground")} />
+      {calendar?.label ?? `Kalender ${calendarId}`}
+    </span>
+  );
+}