First off, PNGs do not necessarily slow your site down anymore than a JPG. It all depends on how the image is saved or optimized and the file size. Anyway.
You have a couple options. Since this site is about coding and we don’t support 3rd party plugins I will give you this first.
You can filter the file types the WordPress allows by using upload_mimes. Here is an example of allowing only JPG images.
function wpse_restrict_mimes($mime_types){
$mime_types = array(
'jpg|jpeg' => 'image/jpeg'
);
return $mime_types;
}
add_filter('upload_mimes', 'wpse_restrict_mimes');
Now if someone tries to upload anything other than a JPG they will get a message like this…
This code would go in your theme or better yet Child Theme‘s functions.php file. Keep in mind it will effect the entire site.
You mentioned being a content manager, if your not comfortable with code their are plugins out there that will do this for you. I would suggest using Google to find a couple, read the reviews and make sure the plugin is up-to-date. Something LIKE THIS looks like it may work.