Any native Micro 4/3 lenses that have electrical contacts and can be controlled by the camera through the lens mount should work with the zoom and focus demands and could also be controlled remotely from an ATEM Switcher.
The problem is that there are only 4 native Micro 4/3 lenses that have been designed with internal zoom motors to enable power zoom capability (sometimes called servo zoom or electronic zoom). Here is the list:
https://www.blackmagicdesign.com/support/faq/59009There are lots of Micro 4/3 lenses with electronic control of focus, but the vast majority of these have a manual zoom ring that needs to be operated by hand as they were primarily intended for photography rather than video.
This situation has been the same for several years now (I think the last Micro 4/3 power zoom lens release was the Olympus 14-42mm EZ back in 2014). Perhaps someone can convince Panasonic or Olympus or Sigma or some other lens manufacturer to design a new power zoom lens, but so far there hasn't seemed to be much interest in producing such lenses.
You can find threads on this topic going back to the original versions of the Studio Cameras back in 2014:
viewtopic.php?f=4&t=95317viewtopic.php?f=4&t=41495viewtopic.php?f=4&t=21016