This is probably the easiest method.
If you inspect the <body> tag by pressing F12 in your browser you will see it has a different class for each category. You can use this to target your header element for each specific category.
For example, this will change the image for category 6.
body.category-6 .page-header {
background-image: url( http://styleofchamp.com/wp-content/uploads/2019/04/sabri-tuzcu-190600-unsplash-1.jpg ) !important;
}
Note: You can upload images via the file uploader and then just replace the correct path for the background-image URL.
CSS changes can be added to Appearance > Customize > Additional CSS