Short answer
HubSpot's KB: snooze is only in help desk, not on the ticket record, and needs a Service seat. Snoozed tickets leave main views for the Snoozed view until unsnoozed. With snooze for individuals, only you stop seeing it. Snoozed tickets still count toward capacity limits.
1. Views
Help desk views in my demo portal.

2. Capacity
See capacity and routing.