refactor(frontend): restructure project layout and update API schema

Relocate frontend source code from `next-app/` to `frontend/` to align with the new project structure. This includes removing the old Next.js boilerplate files and establishing a cleaner workspace.

Additionally, updates the OpenAPI specification to include support for the `immich` widget type and its corresponding configuration schema.

- Move frontend files to `frontend/`
- Delete obsolete `next-app/` directory and its configuration
- Add `immich` widget type to `openapi.yaml`
- Update `FrontendPlan.md` with dashboard refactor and UX direction

frontend/components/ui/badge.tsx

@@ -0,0 +1,29 @@
+import * as React from "react";
+import { cva, type VariantProps } from "class-variance-authority";
+import { cn } from "@/lib/utils";
+
+const badgeVariants = cva(
+  "inline-flex items-center rounded-full border px-2 py-0.5 text-[10px] font-medium uppercase tracking-wide transition-colors focus:outline-none focus:ring-2 focus:ring-ring focus:ring-offset-2",
+  {
+    variants: {
+      variant: {
+        default: "border-transparent bg-primary text-primary-foreground",
+        secondary: "border-transparent bg-secondary text-secondary-foreground",
+        destructive: "border-transparent bg-destructive text-destructive-foreground",
+        outline: "text-foreground",
+        local: "border-transparent bg-blue-500/15 text-blue-500",
+        external: "border-transparent bg-emerald-500/15 text-emerald-500",
+        custom: "border-transparent bg-amber-500/15 text-amber-500",
+      },
+    },
+    defaultVariants: { variant: "default" },
+  },
+);
+
+export interface BadgeProps extends React.HTMLAttributes<HTMLDivElement>, VariantProps<typeof badgeVariants> {}
+
+function Badge({ className, variant, ...props }: BadgeProps) {
+  return <div className={cn(badgeVariants({ variant }), className)} {...props} />;
+}
+
+export { Badge, badgeVariants };