webcam video (via chat apps like Zoom)

BlackMagic Web Presenter $600 US

see: https://sofimarshall.com/real-time-remote-editing/
Blackmagic Web Presenter is fed video (and audio) from Avid via HDMI or SDI and sends back a web-cam compatible signal via USB that can be shared on Zoom chat
audio from chat microphone and audio from Avid are combined using $99 Loopback software (sounds similar to SoundFlower)

AVerMedia Live Gamer Portable 2 is fed video (720p/23.976 works, 1080p/23.976 does not) via HDMI from Avid sends back a web-cam compatible signal via USB that can be transmitted via Zoom or FaceTime or Skype
HDMI loops through the device back to client monitor
device has microphone input; audio from Avid HDMI combines with that in web-cam signal
Avid audio sounded bad (tinny) in tests
see: http://storage.avermedia.com/web_release_www/GC510/GC510_Datasheet_20170218.pdf

HDMI in, web-cam out ^[1]
because there is no loop-through, an HDMI splitter would be needed if you needed to send HDMI to your monitor

see: https://www.epscineworks.com/editorial
SDI video from Avid sent to capture card on 2010 Mac Pro running Windows 7 Pro and Adobe Flash Media Live Encoder 3.2 streaming to EPS server that host to EPS password protected web page.

see: https://doc.haivision.com/MakitoXEnc2.3
encoding box at editor's end and decoding box at producer's end connected to monitor
one-to-one video transmission
SDI input and ethernet port on editor's end
HDMI output and ethernet port on producer's end
configured via IP web interface