Great question! I am the harmony queen (!) and my students probably think I’m weirdly obsessed with getting them to chuck a harmony on to every bloody chorus they record in a song!
However, I could really do with finding out about harmony exercises! I should know this as a choir leader too… I have done some scales in harmony (e.g. I sing G-G and get the student to sing the 3rd above, then we swap) and teach a bit of theory… that’s it really!