My AGPL app Jonline does what your customer wants. Every conversation has “discussion” (most recent at top) or “chat” mode, and you can star any reply at any depth to have it accessible from a menu. (TODO: push notifications, but when they’re done, starred posts/replies will also support them.)

Here’s a sample convo where you can try out the functionality: https://jonline.io/post/4zHQSj