Is a covenant with Allah not to listen to music considered broken when one unintentionally hears it in public places or educational videos, knowing that hearing it in these situations is not by choice?

A Muslim is not considered a breaker of a covenant merely by hearing involuntarily. Rather, they become a breaker of it by intentionally listening. So, if a Muslim is in a place where music is being played and did not intend to listen to it, or encountered music while searching for something else, that does not harm them. However, if the music is mixed with the content creator's speech, the volume must be lowered when the music plays, and it is preferable to seek content free of music or a program to remove it.