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/public-calendar.test.ts

@@ -0,0 +1,85 @@
+import { afterEach, describe, expect, it, vi } from "vitest";
+import {
+  fetchUpcomingPublicEvents,
+  googleCalendarUrl,
+  icalUrl,
+  selectUpcoming,
+  toGoogleCalendar,
+  toWebcal,
+  webcalUrl,
+} from "@/lib/public-calendar";
+import type { ApiEvent } from "@/lib/types";
+
+const now = new Date("2026-09-28T10:00:00Z");
+
+const row = (eventId: number, start: string, end: string, name = `E${eventId}`): ApiEvent => ({
+  eventId,
+  calendarId: 1,
+  uuid: `u${eventId}`,
+  name,
+  description: "",
+  startDateTime: start,
+  endDateTime: end,
+  createdDate: null,
+  location: "",
+  url: "",
+  wholeDay: 0,
+  repeatFrequency: "",
+});
+
+afterEach(() => {
+  vi.unstubAllGlobals();
+});
+
+describe("subscription links", () => {
+  it("builds the iCal, webcal and Google links from the API URL", () => {
+    expect(icalUrl("https://api.nachklang.art")).toBe("https://api.nachklang.art/calendar/events/public/ical");
+    expect(webcalUrl("https://api.nachklang.art")).toBe("webcal://api.nachklang.art/calendar/events/public/ical");
+    expect(webcalUrl("http://localhost:3000")).toBe("webcal://localhost:3000/calendar/events/public/ical");
+    // The same link the Angular landing page hardcoded.
+    expect(googleCalendarUrl("https://api.nachklang.art")).toBe(
+      "https://calendar.google.com/calendar/r?cid=webcal%3A%2F%2Fapi.nachklang.art%2Fcalendar%2Fevents%2Fpublic%2Fical",
+    );
+  });
+});
+
+describe("links for a password-protected calendar", () => {
+  it("keeps the password through the webcal and Google conversions", () => {
+    const ical = "https://api.nachklang.art/calendar/events/choir/ical?password=a%26b";
+    expect(toWebcal(ical)).toBe("webcal://api.nachklang.art/calendar/events/choir/ical?password=a%26b");
+    // Encoded once more as a whole, so Google hands back exactly the URL above.
+    const cid = new URL(toGoogleCalendar(ical)).searchParams.get("cid");
+    expect(cid).toBe("webcal://api.nachklang.art/calendar/events/choir/ical?password=a%26b");
+  });
+});
+
+describe("selectUpcoming", () => {
+  it("keeps events not yet over, earliest first, up to the limit", () => {
+    const rows = [
+      row(1, "2026-11-01T18:00:00Z", "2026-11-01T20:00:00Z"),
+      row(2, "2026-07-01T18:00:00Z", "2026-07-01T20:00:00Z"), // over
+      row(3, "2026-09-28T06:00:00Z", "2026-09-28T07:00:00Z"), // earlier today: still listed
+      row(4, "2026-10-01T18:00:00Z", "2026-10-01T20:00:00Z"),
+    ];
+    expect(selectUpcoming(rows, now, 2).map((e) => e.eventId)).toEqual([3, 4]);
+  });
+});
+
+describe("fetchUpcomingPublicEvents", () => {
+  it("returns null instead of throwing when the API is unreachable or unhappy", async () => {
+    vi.stubGlobal("fetch", vi.fn().mockRejectedValue(new TypeError("fetch failed")));
+    await expect(fetchUpcomingPublicEvents("https://api.test", now, 3)).resolves.toBeNull();
+    vi.stubGlobal("fetch", vi.fn().mockResolvedValue(new Response("{}", { status: 500 })));
+    await expect(fetchUpcomingPublicEvents("https://api.test", now, 3)).resolves.toBeNull();
+  });
+
+  it("parses what the public feed returns", async () => {
+    const fetch = vi.fn().mockResolvedValue(
+      new Response(JSON.stringify([row(1, "2026-11-01T18:00:00Z", "2026-11-01T20:00:00Z")]), { status: 200 }),
+    );
+    vi.stubGlobal("fetch", fetch);
+    const events = await fetchUpcomingPublicEvents("https://api.test", now, 3);
+    expect(events?.map((e) => e.eventId)).toEqual([1]);
+    expect(fetch).toHaveBeenCalledWith("https://api.test/calendar/events/public/json", { next: { revalidate: 300 } });
+  });
+});