abdellatif-laghjaj/laravel-chat-app ? reverse-engineered prompt

Build me a simple private chat app where people can sign up, log in, and message each other one on one in real time.

I want a clean chat screen with a list of users or conversations on the side, the selected conversation in the main area, and messages appearing instantly without refreshing. New messages should be saved, loaded from the database, and delivered live using Laravel broadcasting with Pusher and Echo. Please make the frontend feel modern and simple, and use the existing Laravel and Vue setup in this project.

Set up the basic auth flow, user list, chat messages, send message form, and the real time updates. If there are any missing details or current docs I should check, look them up online and use the best current approach. Make sure it works smoothly end to end and is ready to run locally with the usual environment settings.