From John Gruber's write up on how he recorded and produced this video version of The Talk Show with Craig Federighi and Greg Joswiak of Apple:
Basically, the secret to shooting a remote interview that doesn’t look like a recorded internet call is not to simply record the internet call. Instead, shoot each participant like you would if there were no internet call involved, recording video and audio locally for everyone, using decent cameras and microphones.
I dig this part about the video camera choices:
For video, we shot 4K 30 FPS using iPhone 11 Pros. That’s right, iPhones. Apple seems to have plenty of them so Federighi and Joz each had two — one positioned head-on, and one to the side for a wider-angle view. I just used one.
Apple certainly has the budget and ability to bring in any camera in the world. And obviously there's a marketing angle to using their own product. But interestingly enough, they chose to use Cisco's Webex for the actual call instead of FaceTime, even though everyone on the call was on iPads and a Mac laptop.
The iPhone 11 - and especially the iPhone 11 Pro - is an amazing video camera. It's not a Blackmagic Pocket Cinema, but it's likely you already have access to one if you're trying to record a video or live stream.