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/ui/input.tsx

@@ -0,0 +1,19 @@
+import * as React from "react"
+import { Input as InputPrimitive } from "@base-ui/react/input"
+import { cn } from "@/lib/utils"
+
+function Input({ className, type, ...props }: React.ComponentProps<"input">) {
+  return (
+    <InputPrimitive
+      type={type}
+      data-slot="input"
+      className={cn(
+        "h-9 w-full min-w-0 rounded-3xl border border-transparent bg-input/50 px-3 py-1 text-base transition-[color,box-shadow,background-color] outline-none file:inline-flex file:h-7 file:border-0 file:bg-transparent file:text-sm file:font-medium file:text-foreground placeholder:text-muted-foreground focus-visible:border-ring focus-visible:ring-3 focus-visible:ring-ring/30 disabled:pointer-events-none disabled:cursor-not-allowed disabled:opacity-50 aria-invalid:border-destructive aria-invalid:ring-3 aria-invalid:ring-destructive/20 md:text-sm dark:aria-invalid:border-destructive/50 dark:aria-invalid:ring-destructive/40",
+        className
+      )}
+      {...props}
+    />
+  )
+}
+
+export { Input }