This works with the help of the following code in functions.php:
function filter_site_upload_size_limit( $size ) {
if ( ! current_user_can( 'manage_options' ) ) {
$size = 1024 * 4000; // max. 4 MB
}
return $size;
}
add_filter( 'upload_size_limit', 'filter_site_upload_size_limit', 20 );