I believe Absil, Mahony, and Sepulchre also have a book on optimization over manifolds:

https://press.princeton.edu/absil

I was unaware of the Bournal work, so thanks for that. Do you have any idea how Bournal's approach differs from Absil's?

For others, it looks like Bournal also has a book on the topic from 2023:

https://www.nicolasboumal.net/book/