Harvard does offer a free course on U.S. government basics. It is called "American Government: Constitutional Foundations." Professor Thomas E. Patterson says in the opening video that the U.S. Constitution "marked the founding of a new form of government. One based on the consent of the governed, rather than the dictates of the king." In this way, the course educates on the differences between America's "limited government" and historical monarchy. While "spotting dictatorship" is not necessarily a key component of the course, understanding American personal freedoms and civil liberties granted by the U.S. governmental structure can inform students of how the American system differs from dictatorship.
The course has been regularly starting new sessions since its inception in 2018. The latest started on May 27, 2025, and the next begins today, June 1st. Therefore, it is only a correlation that the course is running after recent Trump actions. The course description does not explicitly state that it covers Trump administration actions, but it indicates that contemporary issues, such as affirmative action, and rights held by Americans today, as well as challenges to those rights, are part of the curriculum.
https://www.snopes.com/fact-check/harvard-constitution-course/
https://www.edx.org/learn/government/harvard-university-american-government-constitutional-foundations