Don't forget that most cameras that have detachable lenses do not even have all that information present of the lens.
With broadcast these lenses normally do not comunicate this back to the camera. And with photolenses some info is given to the camera. But photolenses often do not support zoom control.
Hanc (Horizontal Ancilary data) & Vanc (Vertical Ancilary data) is data embedded into the sdi information.
This data can be Timecode, Record flags, Embedded Audio, Closed caption, DVITC, Dolby Meta data, payload id's, ETC ,
And BMD cleverly uses a bit of Anc data to move control data from the Atem to the BMD Camera's. (which is not done by any other manufacturer. )
https://en.wikipedia.org/wiki/Ancillary_dataBut there is no return data to the Atem. So it is not use-able for your case.
The Eva-1 also does not have a lot of information that is embedded into there ANC data.
So while your idea is great.. There is a reason those virtual studio setups with AR cost so much.. As they add sensors to the camera and put in very expensive lenses that have 12 bit reading on there focus and zoom. This is then all processed by a controller that changes that to a position in time and space.