Short answer
HubSpot's KB: DMs are Instagram only and on the web, not the mobile app. On connecting or reconnecting, only the last 7 days are retrieved. Outgoing DMs show only after the recipient replies. First-time setup needs a disconnect and reconnect.
1. In HubSpot
The relevant screen in my demo portal.

2. Worth knowing
Reconnect early so the 7-day window doesn't drop older threads.