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>

docs/features.md

@@ -0,0 +1,49 @@
+# Features
+
+What the calendar app does, as of the Next.js rewrite (September 2026).
+
+## Public page (`/`)
+
+- Subscribe to the public calendar: Apple Kalender (`webcal://`), Google Kalender (deep link), or
+  copy the iCal URL (shows the URL if the clipboard isn't available).
+- "Nächste Termine": the next four public events with date, time and place; an event with a web
+  link opens it. Refreshed every five minutes; hidden if the API can't be reached.
+- Link to the Verwaltung (`/admin`).
+
+## Verwaltung (`/admin`)
+
+Sign-in happens in the admin app (one account for all Nachklang apps). Accounts need the calendar
+permission; without it the page says so instead of redirecting.
+
+**List**
+- All calendars in one list, grouped by month, colour-coded per calendar.
+- Calendar chips toggle calendars on and off, with a count each; Geburtstage is off by default.
+- Kommend / Vergangen / Alle. "Vergangen" shows the newest first; "Alle" scrolls to a "Heute" marker.
+- Search over title and location.
+- Sort by start or by creation date (the latter as a flat list).
+- The view is in the URL, so a link reproduces it.
+- Drafts show an "Entwurf" badge and a "Veröffentlichen" button, which asks for confirmation and
+  says who will see the event.
+- Repeating events (birthdays) show a "jährlich" badge and appear at their next occurrence.
+- Failed calendars are marked on their chip with a retry banner; the rest of the list stays usable.
+
+**Edit sheet** (bottom sheet on phones, side panel on larger screens)
+- Create ("Neuer Termin" in the header, "+" button on phones), edit, duplicate, delete.
+- Fields: Kalender, Titel, Ganztägig, Beginn, Ende, Ort, Link, Beschreibung (multi-line), Status
+  (Entwurf / Veröffentlicht; "Privat" is kept but not selectable).
+- Moving the start moves the end with it. Whole-day events take dates only.
+- A link without `https://` is completed; anything that isn't a web address is flagged.
+- Moving an event into Geburtstage makes it yearly; moving it out removes that again.
+- Errors appear next to their field; a failed save keeps the edits and says why.
+- Closing with unsaved changes asks first; so does leaving the page.
+- Shows who created and last changed the event.
+
+**Abonnieren** (header)
+- Subscription links for every calendar, including the internal ones with their password: Apple,
+  Google, or copy. Chor and Geburtstage share a password.
+
+## Not (yet) possible
+
+- Restoring deleted events and editing recurrence need API work first - see
+  [api-wishlist.md](api-wishlist.md).
+- A month-grid view was deferred (decision Q6); the agenda list came first.