EventSub is very similar to Webhooks, but it doesn’t follow the Websub spec which gives it more freedom than Webhooks.
Websockets are mentioned because while EventSub currently only supports HTTPS callbacks, it will eventually be possible to subscribe to events and have Twitch send notifications back through other transport methods, such as Websockets, or SNS, etc…
One of the key changes for the issue you’re facing though is that EventSub uses App tokens entirely, and the subscriptions aren’t limited by token life, meaning that once you subscribe to a topic you’ll stay subscribed until you cancel it or you no longer have authorization for that topic.