The only way I've seen this done with professional kit it to literally run all your cameras and monitors mounted on their sides. Then use a software encoder to do the rotation and stream it at the 9:16 ratio.
There's basically no professional support for 9:16 aspect ratios - SDI certainly didn't, and I don't think even HDMI has support for it (9:16 images from computers are sent as 16:9 data with the content rotated, or as pillarboxed, shrunken images into a 16:9 feed from phones). So you can't get a 9:16 images in or out of an Atem, even if the Atem itself supported the aspect ratio!
If you rotate in the mixer, you also reduce your resolution by nearly 3/4, and you'll still end up with 16:9 video coming out of the switcher - which will then be displayed as a postage stamp on a phone in portrait mode.
Edit to add - this is how they produced a dedicated portrait video coverage of a German football match -
https://www.svgeurope.org/blog/headline ... rait-mode/