Is attending courses that include music during video presentations considered a sin, and does it obligate me to leave the hall or advise the trainer, and does that affect benefiting from the rest of the course content?

It is permissible to attend courses whose content is permissible and beneficial. If a course includes objectionable matters such as musical instruments or an invitation to a forbidden act, there is no harm in attending it out of necessity, while disapproving of it in one's heart. A distinction should be made between unintentionally hearing musical instruments and intentionally listening to them. It is incumbent to enjoin good and forbid evil, and to advise the trainer if possible.