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>

components/ui/badge.tsx

@@ -0,0 +1,51 @@
+import { mergeProps } from "@base-ui/react/merge-props"
+import { useRender } from "@base-ui/react/use-render"
+import { cva, type VariantProps } from "class-variance-authority"
+import { cn } from "@/lib/utils"
+
+const badgeVariants = cva(
+  "group/badge inline-flex h-5 w-fit shrink-0 items-center justify-center gap-1 overflow-hidden rounded-3xl border border-transparent px-2 py-0.5 text-xs font-medium whitespace-nowrap transition-all focus-visible:border-ring focus-visible:ring-[3px] focus-visible:ring-ring/50 has-data-[icon=inline-end]:pr-1.5 has-data-[icon=inline-start]:pl-1.5 aria-invalid:border-destructive aria-invalid:ring-destructive/20 dark:aria-invalid:ring-destructive/40 [&>svg]:pointer-events-none [&>svg]:size-3!",
+  {
+    variants: {
+      variant: {
+        default: "bg-primary text-primary-foreground [a]:hover:bg-primary/80",
+        secondary:
+          "bg-secondary text-secondary-foreground [a]:hover:bg-secondary/80",
+        destructive:
+          "bg-destructive/10 text-destructive focus-visible:ring-destructive/20 dark:bg-destructive/20 dark:focus-visible:ring-destructive/40 [a]:hover:bg-destructive/20",
+        outline:
+          "border-border text-foreground [a]:hover:bg-muted [a]:hover:text-muted-foreground",
+        ghost:
+          "hover:bg-muted hover:text-muted-foreground dark:hover:bg-muted/50",
+        link: "text-primary underline-offset-4 hover:underline",
+      },
+    },
+    defaultVariants: {
+      variant: "default",
+    },
+  }
+)
+
+function Badge({
+  className,
+  variant = "default",
+  render,
+  ...props
+}: useRender.ComponentProps<"span"> & VariantProps<typeof badgeVariants>) {
+  return useRender({
+    defaultTagName: "span",
+    props: mergeProps<"span">(
+      {
+        className: cn(badgeVariants({ variant }), className),
+      },
+      props
+    ),
+    render,
+    state: {
+      slot: "badge",
+      variant,
+    },
+  })
+}
+
+export { Badge, badgeVariants }