The best way to share a YouTube, Vimeo, or Canvas Studio video is through the built-in Share external video option.
However, if you want to use the Screen sharing to share a video (start screen sharing and then play the video on your screen outside of BigBlueButton), then we recommend using Mac OS X and the Chrome browser.
When you share your screen using Mac OS X + Chrome, viewers will also hear the audio from the video.
However, if you try the same on Windows, the audio will not come through. Students will see the video through screen sharing, but will not hear any audio.
(Update 2020-09-26) We are working on adding support later this fall for capturing the system audio on Windows when sharing the screen.