I had to dig around a bit, but I found the reason the popup wasn’t appearing when trying to start the share.
This post about user deny screen share is what ultimately wound up being the solution.
I didn’t realize that there had to be a gesture associated with the screen share whereas Chrome allows you to init, join, and start share all in sequence without any human intervention.
So basically,
- Init and join session
- display a button to trigger the share
- start share on click of the ‘Share’ button