8:30 hour stopover Beijing International

The round trip to the city center may take 2.5-3h. So you may have 3 hours in downtown to explore Forbidden City. You can book the ticket in advance on this page: https://www.travelchinaguide.com/attraction/beijing/forbidden-city/tickets-booking.htm
If you don't want to book the ticket, I more recommend Jingshan Park where you can climb to the top to have a bird view of Forbidden City, and walk to explore local food at the nearby Nanluoguxiang.