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/event-display.ts

@@ -0,0 +1,92 @@
+import { berlinDay, formatTime, TIME_ZONE } from "@/lib/dates";
+import { effectiveStart, isRecurring, type Sort } from "@/lib/filter";
+import type { CalendarEvent } from "@/lib/types";
+
+/**
+ * How an event reads in the list. Pure, so the German wording is testable.
+ * All of it is about the *effective* occurrence: a birthday shows this year's
+ * date, not the year of birth.
+ */
+
+const LOCALE = "de-DE";
+const part = (options: Intl.DateTimeFormatOptions) => new Intl.DateTimeFormat(LOCALE, { timeZone: TIME_ZONE, ...options });
+const weekdayFormat = part({ weekday: "short" });
+const dayFormat = part({ day: "numeric" });
+const monthFormat = part({ month: "short" });
+const dayMonthFormat = part({ day: "numeric", month: "short" });
+
+export interface DateBlock {
+  /** "Sa" */
+  weekday: string;
+  /** "3" */
+  day: string;
+  /** "Okt" */
+  month: string;
+}
+
+export const dateBlock = (instant: Date): DateBlock => ({
+  weekday: weekdayFormat.format(instant),
+  day: dayFormat.format(instant),
+  month: monthFormat.format(instant),
+});
+
+/** The occurrence the list shows: start moved to the next repeat, end moved by the same amount. */
+export const occurrence = (event: CalendarEvent, now: Date): { start: Date; end: Date } => {
+  const start = effectiveStart(event, now);
+  const shift = start.getTime() - event.start.getTime();
+  return { start, end: new Date(event.end.getTime() + shift) };
+};
+
+/**
+ * "19:00–21:00 Uhr", "Ganztägig", "Ganztägig · 17.–19. Okt.",
+ * "3. Okt., 19:00 – 5. Okt., 12:00".
+ */
+export const describeWhen = (event: CalendarEvent, now: Date): string => {
+  const { start, end } = occurrence(event, now);
+  const sameDay = berlinDay(start) === berlinDay(end);
+
+  if (event.wholeDay) {
+    return sameDay ? "Ganztägig" : `Ganztägig · ${dayMonthFormat.formatRange(start, end)}`;
+  }
+  if (sameDay) {
+    return `${formatTime(start)}–${formatTime(end)} Uhr`;
+  }
+  return `${dayMonthFormat.format(start)}, ${formatTime(start)} – ${dayMonthFormat.format(end)}, ${formatTime(end)}`;
+};
+
+/** Over before today (Berlin). Repeating events never are. */
+export const isPast = (event: CalendarEvent, now: Date): boolean =>
+  !isRecurring(event) && berlinDay(event.end) < berlinDay(now);
+
+/**
+ * Where "today" falls in a list sorted by start: the index of the event the
+ * "Heute" marker goes in front of, or `events.length` for after the last one.
+ * Ascending, that is the first event not yet over; descending, the first one
+ * that is. Null for a list that isn't ordered by start, or an empty one.
+ */
+export const todayMarkerIndex = (events: readonly CalendarEvent[], sort: Sort, now: Date): number | null => {
+  if (events.length === 0 || sort.startsWith("created")) {
+    return null;
+  }
+  const lookingFor = sort === "start_desc";
+  const index = events.findIndex((e) => isPast(e, now) === lookingFor);
+  return index === -1 ? events.length : index;
+};
+
+/** The badge for a repeat frequency; "" for none. Unknown values are shown as they are. */
+export const repeatLabel = (repeatFrequency: string): string => {
+  switch (repeatFrequency) {
+    case "":
+      return "";
+    case "YEARLY":
+      return "jährlich";
+    case "MONTHLY":
+      return "monatlich";
+    case "WEEKLY":
+      return "wöchentlich";
+    case "DAILY":
+      return "täglich";
+    default:
+      return repeatFrequency.toLowerCase();
+  }
+};