Just to leave registered, I tested the 'copy and paste' way to solve this problem in a real video call yesterday (using Opera GX, only) and I it didn't work unfortunately, although it doesn't seem to be a Opera GX's fault.
I was on a actual video call with a friend and everything was going well with the popup window, so I have copied and pasted the window's link in a new tab and the video call loaded perfectly (at the new tab). But right after the loading was finished I had to click on Hangout's button saying Join the meeting or something close to that. After click on it, I was duplicated, i. e., there were two of me and one of my friend on the calling (no problem though) and I could make me be listened and seen, but I was able to only see my friend, not to listen to him... that was the real problem.
After some tries we gave up from this solution and continued to use two windows separately.