add alt text to images loaded from json with media_sideload_image

Once you have the attachment ID you can add alt text by setting the _wp_attachment_image_alt post meta for the attachment:

update_post_meta( $attachment_id, '_wp_attachment_image_alt', 'Alt text here' );

To get the attachment ID from media_sideload_image() you can set the 4th argument to 'id':

$attachment_id = media_sideload_image( $file, $post_id, $desc, 'id' );

if ( ! is_wp_error( $attachment_id ) ) {
    update_post_meta( $attachment_id, '_wp_attachment_image_alt', 'Alt text here' );
}