Short answer
HubSpot's KB: a calling app appears as a calling remote and window, remote only, or a calling widget. You can't navigate away while a widget is in use. You can't call from a custom object record with a calling app.
1. In HubSpot
The relevant screen in my demo portal.

2. Worth knowing
In-call and after-call features vary by provider.
3. Related
Inbound calls and HubSpot numbers.