feat(analytics): add behavior and payment funnel tracking

src/app/chat/components/chat-header.tsx

@@ -25,6 +25,8 @@ export function ChatHeader({ isGuest, offerBanner }: ChatHeaderProps) {
       {isGuest ? (
         <button
           type="button"
+          data-analytics-key="chat.open_signup"
+          data-analytics-label="Open sign up"
           className="flex w-full cursor-pointer items-center justify-center gap-(--spacing-sm,8px) border-0 bg-(--color-accent,#f84d96) px-(--spacing-md,12px) py-(--spacing-sm,8px) text-center text-(length:--responsive-caption,var(--font-size-sm,12px)) font-medium text-white"
           onClick={() => navigator.openAuth(ROUTES.chat)}
           aria-label="Sign up to unlock more features"
@@ -46,10 +48,13 @@ export function ChatHeader({ isGuest, offerBanner }: ChatHeaderProps) {
             href={ROUTES.splash}
             variant="dark"
             ariaLabel="Back to home"
+            analyticsKey="chat.back_to_home"
           />
 
           <button
             type="button"
+            data-analytics-key="chat.open_menu"
+            data-analytics-label="Open chat menu"
             className="flex size-(--responsive-icon-button-size,42px) cursor-pointer items-center justify-center rounded-(--radius-full,999px) border border-[rgba(255,255,255,0.12)] bg-[rgba(13,11,20,0.7)] text-(--color-text-primary,#fff) shadow-[0_10px_24px_rgba(0,0,0,0.2)] backdrop-blur-md transition-[background,transform] duration-150 hover:bg-[rgba(28,24,39,0.82)] active:scale-96 focus-visible:outline-2 focus-visible:outline-offset-3 focus-visible:outline-[#f657a0]"
             onClick={() => navigator.push(ROUTES.sidebar)}
             aria-label="Menu"