Real Estate Map & Chat Enhancements

I want to enrich my current real-estate website with four tightly-integrated upgrades:

• Interactive property map
Google Maps must display every listing, allow cluster or pin views, and let visitors draw or click to filter by area.
• “Save to Favorites” workflow
A logged-in visitor needs a one-click way to add or remove any listing from a personal wishlist that is recalled on their next visit. If cross-device sync feels heavy for the first release, we can discuss a phased approach.
• Built-in buyer/agent messaging
A lightweight real-time chat pane should open straight from each listing so a buyer can talk to the assigned agent without leaving the page; think socket.io or Firebase-style push for instant delivery and read status.
• Mobile-first speed tuning
Pages must pass Core Web Vitals on mobile, tablet, and desktop once the new code is in place.

Key acceptance criteria
– Map loads within 2 s on 4G and returns filtered results instantly.
– Wishlist persists after logout/login and survives page refresh.
– Chat notifications reach both parties in real time and store all threads in the database.
– No existing user accounts, listing search, or agent profile data are lost.

Please build clean, documented code (NextJs, React, Tailwind)