feat: enhance YouTube chat ingestion with support for gift memberships

Expand YouTube chat ingestion to handle membership gift events including purchases and redemptions. Update SuperChat extraction to support multiple paid message types and improve field name handling. Display membership level in overlay for gift events.

client/app/overlay/page.tsx

@@ -91,7 +91,7 @@ export default function OverlayPage() {
           )}
           {message.membershipGift && (
             <div className="overlay__membership">
-              🎁 New Member!
+              🎁 {message.membershipLevel || 'New Member'}
             </div>
           )}
           <p className="overlay__text">{message.text}</p>