clean HDMI output camera - on start
First: 4k for livestreaming is pretty overkill. Please remember that your streaming device (your computer) and internet upload speed need handle this... AND to top things of not all of your viewers will be able to watch the stream in 4k because of their internet and missing out 4k devices.
Alpha Gaming (Harris Heller) is covering everything you want to know about cameras (and livestreaming) in video form on youtube.
Here are the most popular (and very professional but &quot;only&quot; 1080p not 4k) cameras for livestreaming with very helpful information: a sony should be your choice
And here are some additional information for you before you choose your camera and lense: equipment all around your camera
IMHO, this should be your question: How much FOV (field of view) and DOF (depth of field) do you want?
If you really want to live stream in 4k (only 30 fps) then the SONY A6100 should be a good choice.