Add Umami analytics, subscription tiers, tool-call metering

- Analytics: <Analytics /> in root layout loads umami when NEXT_PUBLIC_UMAMI_* env are set
- Subscription: free/pro tiers in Postgres, daily quotas (10msg/5tool free, 1000/500 pro)
- Chat route: checkAndConsume(chat_message) gate before streamText, 429 when exhausted
- Tool metering: getWeather wrapped with withLimit decorator that deducts tool_call quota
- Pricing page at /pricing with upgrade button
- /api/billing/checkout posts to EGBE payment gateway, /api/billing/webhook verifies HMAC and upgrades user on checkout.session.completed
- UsageBadge in chat header polls /api/usage every 15s
- Dropped now-unused entitlements.ts

components/chat/chat-header.tsx

@@ -1,11 +1,10 @@
 "use client";
 
 import { PanelLeftIcon } from "lucide-react";
-import Link from "next/link";
 import { memo } from "react";
 import { Button } from "@/components/ui/button";
 import { useSidebar } from "@/components/ui/sidebar";
-import { VercelIcon } from "./icons";
+import { UsageBadge } from "./usage-badge";
 import { VisibilitySelector, type VisibilityType } from "./visibility-selector";
 
 function PureChatHeader({
@@ -34,15 +33,6 @@ function PureChatHeader({
         <PanelLeftIcon className="size-4" />
       </Button>
 
-      <Link
-        className="flex size-8 items-center justify-center rounded-lg md:hidden"
-        href="https://vercel.com/templates/next.js/chatbot"
-        rel="noopener noreferrer"
-        target="_blank"
-      >
-        <VercelIcon size={14} />
-      </Link>
-
       {!isReadonly && (
         <VisibilitySelector
           chatId={chatId}
@@ -50,19 +40,9 @@ function PureChatHeader({
         />
       )}
 
-      <Button
-        asChild
-        className="hidden rounded-lg bg-foreground px-4 text-background hover:bg-foreground/90 md:ml-auto md:flex"
-      >
-        <Link
-          href="https://vercel.com/templates/next.js/chatbot"
-          rel="noopener noreferrer"
-          target="_blank"
-        >
-          <VercelIcon size={16} />
-          Deploy with Vercel
-        </Link>
-      </Button>
+      <div className="ml-auto flex items-center gap-2">
+        <UsageBadge />
+      </div>
     </header>
   );
 }