What is the ruling on publishing beneficial technical videos that contain background music, and what is the responsibility for allowing their publication? Is earning from this work permissible, knowing that the goal is to spread knowledge and not music?

Music is forbidden by the consensus of scholars, and there is no difference between its various types. Listening to educational clips that contain background music, and spreading them, is forbidden because it constitutes aiding in sin. The spreading of these clips must be prevented. If the administrator is unable to do so, it is better to relinquish the administration of the group. However, what the administrator earns from their administration is not forbidden due to members spreading those clips.