Hi @zen-dsgnr I have tested this since we use Kaltura as well. I cannot go to a discussion in a group and add content published to the course gallery, but I am able to go to the main discussion in the course > edit the topic and insert a video published to the gallery. Groups are not completely connected to a course. You cannot directly access course materials from within a group. If you insert the video into the main discussion topic in the course, students will see it in the discussion topic in their group environment.
As a workaround, I was able to copy the embed code for a video I inserted temporarily into other Canvas content and paste it into a group discussion topic.