Short answer
HubSpot's KB: a Slack admin may need to reconnect the app. In channels and threads, Breeze replies only when @mentioned each time. With several HubSpot accounts connected, pick one. It works with standard and custom objects.
1. In HubSpot
The relevant screen in my demo portal.

2. Worth knowing
Use the Messages tab for longer back-and-forth.
3. Related
Slack integration and Breeze Assistant.