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/types.ts

@@ -0,0 +1,86 @@
+/**
+ * Shapes on the wire and in the app.
+ *
+ * `ApiEvent` is what `GET /calendar/events/:calendar/json` actually returns,
+ * which is looser than the API's own `Event` interface claims: the service maps
+ * raw MariaDB rows straight through (`toEvent` in events.service.ts), so
+ * `wholeDay` arrives as whatever the driver produced for the column (1/0 rather
+ * than true/false is the likely case), and a deleted event's latest version is
+ * a row with only `status` set - every other version column is null. `status`
+ * is missing entirely from the anonymous public listing.
+ *
+ * `CalendarEvent` is the parsed, trustworthy form everything else in the app
+ * works with. Parsing happens once, in `parseApiEvent`.
+ */
+
+export type EventStatus = "PUBLIC" | "PRIVATE" | "DRAFT" | "DELETED";
+
+export interface ApiEvent {
+  eventId: number;
+  calendarId: number;
+  uuid: string;
+  name: string | null;
+  description: string | null;
+  startDateTime: string | null;
+  endDateTime: string | null;
+  createdDate: string | null;
+  lastModifiedDate?: string | null;
+  location: string | null;
+  createdBy?: string | null;
+  lastModifiedBy?: string | null;
+  url: string | null;
+  wholeDay: boolean | number | null;
+  repeatFrequency: string | null;
+  status?: string | null;
+}
+
+export interface CalendarEvent {
+  eventId: number;
+  calendarId: number;
+  uuid: string;
+  name: string;
+  description: string;
+  /** Instants. Wall-clock meaning is always Europe/Berlin, see lib/dates.ts. */
+  start: Date;
+  end: Date;
+  created: Date | null;
+  lastModified: Date | null;
+  location: string;
+  createdBy: string;
+  lastModifiedBy: string;
+  url: string;
+  wholeDay: boolean;
+  /** "" when the event does not repeat. Sent to iCal verbatim as RRULE:FREQ=… */
+  repeatFrequency: string;
+  status: EventStatus;
+}
+
+/**
+ * The body of POST /calendar/events, PUT /calendar/events/:id and
+ * PUT /calendar/events/move/:id.
+ *
+ * Every field is required here on purpose. PUT replaces the whole version and
+ * defaults whatever is missing - `repeatFrequency ?? ''`, `status ?? 'PUBLIC'`
+ * (events.router.ts) - so a partial body silently drops a birthday's
+ * recurrence or publishes a draft.
+ */
+export interface EventPayload {
+  calendarId: number;
+  name: string;
+  description: string;
+  startDateTime: string;
+  endDateTime: string;
+  location: string;
+  url: string;
+  wholeDay: boolean;
+  repeatFrequency: string;
+  status: EventStatus;
+}
+
+/** GET /admin/me - the signed-in account, shared by all Nachklang apps. */
+export interface AdminUser {
+  id: string;
+  email: string;
+  fullName: string;
+  apps: string[];
+}