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>

.gitignore

@@ -1,43 +1,42 @@
-# See http://help.github.com/ignore-files/ for more about ignoring files.
+# See https://help.github.com/articles/ignoring-files/ for more about ignoring files.
 
-# Compiled output
-/dist
-/tmp
-/out-tsc
-/bazel-out
-
-# Node
+# dependencies
 /node_modules
-npm-debug.log
-yarn-error.log
+/.pnp
+.pnp.*
+.yarn/*
+!.yarn/patches
+!.yarn/plugins
+!.yarn/releases
+!.yarn/versions
 
-# IDEs and editors
-.idea/
-.vscode/
-.project
-.classpath
-.c9/
-*.launch
-.settings/
-*.sublime-workspace
-
-# Visual Studio Code
-.vscode/*
-!.vscode/settings.json
-!.vscode/tasks.json
-!.vscode/launch.json
-!.vscode/extensions.json
-.history/*
-
-# Miscellaneous
-/.angular/cache
-.sass-cache/
-/connect.lock
+# testing
 /coverage
-/libpeerconnection.log
-testem.log
-/typings
 
-# System files
+# next.js
+/.next/
+/out/
+
+# production
+/build
+
+# misc
 .DS_Store
-Thumbs.db
+*.pem
+
+# debug
+npm-debug.log*
+yarn-debug.log*
+yarn-error.log*
+.pnpm-debug.log*
+
+# env files (can opt-in for committing if needed)
+.env*
+!.env.local.example
+
+# vercel
+.vercel
+
+# typescript
+*.tsbuildinfo
+next-env.d.ts