Syncing Server & Clients

Hi everyone,

my Google skills have failed me. I am currently building an application which has a core functionality which is similar to skype or slack. The current technology stack is: MySQL, Golang, Nginx, Traefik for the backend and React for the frontend, all wrapped in Docker and utilizing the Gitlab CI/CD pipelines.

What we'd like to have is a real-time synchronization of clients when something related to them happens. New group including you as a member? => display that, new message? => display that, users going online/offline? => …

How would I solve that? I'm not even sure what to google for that. Is this a use case for MQTT brokers?
Thanks for any opinions and hints!