I have made a lot of updates to the Home Assistant integration. Here's some screenshots showing the entities it will add. Each button and the Hub will act as a separate devices. The click type is an attribute on a binary sensor on a button.
These entities will help you setup automations based on click type and also keep track of when it's time to change the battery, for example.
Once the js-script is added and started on the Hub and the integration is added in HomeAssistant, the Hub will automatically be discovered in Home Assistant and the buttons will be added.
I wish there was a websocket or something similar already built into the Hub, that would make the integration a lot easier to add from a user perspective, at least until Matter support is released.