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/PublishDialog.tsx

@@ -0,0 +1,79 @@
+"use client";
+
+import { LoaderCircleIcon, SendIcon } from "lucide-react";
+import { CalendarBadge } from "@/components/admin/CalendarBadge";
+import {
+  AlertDialog,
+  AlertDialogCancel,
+  AlertDialogContent,
+  AlertDialogDescription,
+  AlertDialogFooter,
+  AlertDialogHeader,
+  AlertDialogTitle,
+} from "@/components/ui/alert-dialog";
+import { Button } from "@/components/ui/button";
+import { calendarById } from "@/lib/calendars";
+import { formatDay } from "@/lib/dates";
+import { describeWhen, occurrence } from "@/lib/event-display";
+import type { CalendarEvent } from "@/lib/types";
+
+/**
+ * "Really publish?" - publishing puts the event into every subscriber's
+ * calendar app, and for the public calendar onto nachklang.art, which is not
+ * something to do by a stray tap on a phone.
+ *
+ * Stays open with a spinner until the API has answered, and stays open on a
+ * failure (the page shows the error as a toast), so a retry is one tap.
+ */
+export function PublishDialog({
+  event,
+  now,
+  publishing,
+  onConfirm,
+  onCancel,
+}: {
+  event: CalendarEvent | null;
+  now: Date;
+  publishing: boolean;
+  onConfirm: (event: CalendarEvent) => void;
+  onCancel: () => void;
+}) {
+  const calendar = event ? calendarById(event.calendarId) : undefined;
+
+  return (
+    <AlertDialog
+      open={event !== null}
+      onOpenChange={(open) => {
+        if (!open && !publishing) onCancel();
+      }}
+    >
+      <AlertDialogContent>
+        {event && (
+          <>
+            <AlertDialogHeader>
+              <AlertDialogTitle>„{event.name}“ veröffentlichen?</AlertDialogTitle>
+              <AlertDialogDescription>
+                {calendar?.slug === "public"
+                  ? "Der Termin wird danach öffentlich angezeigt – auf nachklang.art und bei allen, die den Kalender abonniert haben."
+                  : `Der Termin erscheint danach bei allen, die den Kalender „${calendar?.label ?? event.calendarId}“ abonniert haben.`}
+              </AlertDialogDescription>
+            </AlertDialogHeader>
+            <div className="flex flex-col gap-1.5 rounded-lg bg-muted/60 px-3 py-2.5 text-sm">
+              <span>
+                {formatDay(occurrence(event, now).start)} · {describeWhen(event, now)}
+              </span>
+              <CalendarBadge calendarId={event.calendarId} className="self-start" />
+            </div>
+            <AlertDialogFooter>
+              <AlertDialogCancel disabled={publishing}>Abbrechen</AlertDialogCancel>
+              <Button onClick={() => onConfirm(event)} disabled={publishing}>
+                {publishing ? <LoaderCircleIcon className="animate-spin" /> : <SendIcon />}
+                Veröffentlichen
+              </Button>
+            </AlertDialogFooter>
+          </>
+        )}
+      </AlertDialogContent>
+    </AlertDialog>
+  );
+}