Short answer
HubSpot's KB: the connector respects your HubSpot permissions. ChatGPT shows proposed changes before writing, and actions appear in the Audit Log. Only one HubSpot account connects per ChatGPT account at a time.
1. In HubSpot
The relevant screen in my demo portal.

2. Worth knowing
Users without Super Admin or App Marketplace access need a Super Admin to approve the app first.