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

lib/ai/entitlements.ts

@@ -1,14 +0,0 @@
-import type { UserType } from "@/app/(auth)/auth";
-
-type Entitlements = {
-  maxMessagesPerHour: number;
-};
-
-export const entitlementsByUserType: Record<UserType, Entitlements> = {
-  guest: {
-    maxMessagesPerHour: 10,
-  },
-  regular: {
-    maxMessagesPerHour: 10,
-  },
-};

lib/ai/models.ts

@@ -1,4 +1,4 @@
-export const DEFAULT_CHAT_MODEL = "claude-sonnet";
+export const DEFAULT_CHAT_MODEL = "gpt-5.4-mini";
 
 export type ModelCapabilities = {
   tools: boolean;

lib/ai/tools/with-limit.ts

@@ -0,0 +1,40 @@
+import type { Tool } from "ai";
+import type { LimitKey } from "@/lib/subscription/config";
+import {
+  checkAndConsume,
+  LimitExceededError,
+} from "@/lib/subscription/service";
+
+export function withLimit<T extends Tool>(
+  tool: T,
+  kind: LimitKey,
+  userId: string
+): T {
+  const originalExecute = tool.execute;
+  if (!originalExecute) {
+    return tool;
+  }
+
+  // biome-ignore lint/suspicious/noExplicitAny: wrapper has to be generic across all tool signatures
+  const wrappedExecute = (async (input: any, options: any) => {
+    try {
+      await checkAndConsume(userId, kind);
+    } catch (error) {
+      if (error instanceof LimitExceededError) {
+        return {
+          error: "limit_exceeded",
+          kind: error.kind,
+          tier: error.tier,
+          used: error.used,
+          limit: error.limit,
+          message: `You've hit your ${kind.replace("_", " ")} limit for today (${error.used}/${error.limit} on ${error.tier} tier). Upgrade to Pro for higher limits.`,
+        };
+      }
+      throw error;
+    }
+    return originalExecute(input, options);
+    // biome-ignore lint/suspicious/noExplicitAny: tool execute signature varies
+  }) as any;
+
+  return { ...tool, execute: wrappedExecute } as T;
+}