Add Stripe subscription billing integration

- Add stripe_customer_id and stripe_subscription_id fields to User model
- Add Stripe config settings (secret key, publishable key, price ID, webhook secret)
- Create billing API endpoints: checkout session, webhook handler, portal, status
- Add frontend Billing page with upgrade/manage subscription UI
- Add billing route and Pro nav link
- Add stripe dependency to requirements

backend/app/models/user.py

@@ -18,6 +18,10 @@ class User(Base):
         DateTime(timezone=True), default=lambda: datetime.now(timezone.utc)
     )
 
+    # Stripe
+    stripe_customer_id: Mapped[str | None] = mapped_column(String(255), nullable=True, unique=True)
+    stripe_subscription_id: Mapped[str | None] = mapped_column(String(255), nullable=True)
+
     # Spotify OAuth
     spotify_id: Mapped[str | None] = mapped_column(String(255), nullable=True, unique=True)
     spotify_access_token: Mapped[str | None] = mapped_column(Text, nullable=True)