I would love for you to give CometChat a try! It readily integrates with BuddyPress websites. All it takes is under 10 minutes to set chat up and running on your website.
Unlike other chat solutions, CometChat’s chat functionalities is not restricted to just text chat. Instad it offers voice chat, video chat (both, one on one and group), emojis and stickers, push notifications, email notifications, offline messaging, in built writeboards and whiteboards, in built monetisation features (enabling you to earn money while users chat on your website), auto friend list synchronisation, phone login, social login and so much more!
The above features come at no extra cost! These are included in the pricing tiers you decide to opt for.
CometChat is free to try. You can give it a test drive to see if it fits your requirements.