Do I have to include my pronouns in a course outline?
Instead of the legal aspects, I would like to address the professional and ethical aspects of the pronouns trend.
In my opinion, the purpose of announcing your pronouns is to indicate that you will address other people with respect.  The message that is sent is: since I told you my pronouns, you know that if you tell me how you want to be addressed I will not disrespect that preference.
There is a secondary purpose.  People whose pronouns are not obvious may feel stress because they are the only ones who have to announce their pronouns.  If you announce your pronouns, you are reducing that stress.
Therefore, the professional way to behave is to announce your pronouns.  It's respectful.
Requiring people to announce their pronouns is, however, unethical.  Some people are not sure how they wish to be addressed.  Other people may not feel safe discussing their preferences.  Requiring these people to announce their pronouns is abusive.  Not announcing your pronouns is not necessarily wrong or disrespectful.