Why is Wordpress serving the 1024px version of my image and not the original on a 1920x1080 screen?

The problem seems to be specific to the Twenty Sixteen theme, whose content area I suppose is limited to a maximum width of 840 pixels. The theme adds rules for responsive images in its functions.php, in the twentysixteen_content_image_sizes_attr() function.

function twentysixteen_content_image_sizes_attr( $sizes, $size ) {

    $width = $size[0];

    1200 <= $width && $sizes = '(max-width: 709px) 85vw, (max-width: 909px) 67vw, (max-width: 1362px) 62vw, 1200px';

    if ( 'page' === get_post_type() ) {
        1200 > $width && $sizes = '(max-width: ' . $width . 'px) 85vw, ' . $width . 'px';
    } else {
        1200 > $width && 600 <= $width && $sizes = '(max-width: 709px) 85vw, (max-width: 909px) 67vw, (max-width: 984px) 61vw, (max-width: 1362px) 45vw, 600px';
        600 > $width && $sizes = '(max-width: ' . $width . 'px) 85vw, ' . $width . 'px';
    }

    return $sizes;
}
add_filter( 'wp_calculate_image_sizes', 'twentysixteen_content_image_sizes_attr', 10 , 2 );

I'm honestly not quite sure how to adjust this to support a larger content width, or rather in my case, an image that is always 100% wide, so I'm disabling this for the time being.

For production, it's probably smart to look into this in more detail, though - serving smaller images to smaller-screen devices is certainly a good idea.

Your image's src is pointing to the full size image, so it's not an issue of permalink. The issue happens because of the sizes values. There is a variable that determines the width of your content, which then later WordPress uses to generates the responsive sizes for your images.

This global variable can be set manually in your theme's functions.php file:

if( !isset($content_width) ) {
    $content_width = 1920;
}

You can tweak with this variable to achieve your desired result.

You can check tab media setting in wordpress