You’d have to tweak the top and bottom padding.
It doesn’t crop the image by default (unless the original image is wider than the container width).
Background images aren’t responsive by nature (it’s not a theme thing).
Perhaps try changing the background image position?
https://docs.generatepress.com/article/header-element-overview/#background-image-position
If this doesn’t help, any chance you can duplicate the issue on a live server? It’s really hard for me to tell without looking at it.