I was about to talk about issues with scaling Redis pubsub but apparently they just recently published a newer version (7) with proper sharding support in cluster mode!
You do have to be aware of Redis' limits. But for most sites, "people paying at the moment" is well within them. And Redis is the easiest solution to implement from scratch.
That said, if you're deployed in a cloud, look up cloud specific messaging services. Specifically AWS SNS, Google PubSub and Azure Web PubSub. But the pattern remains the same. The webhook publishes to the PubSub which finds the other end of the websocket which sends information to the client that does something with it.
