Looks like you need to set a User Agent, not 100% as I haven't checked the docs, but setting a User Agent with CURL allows me to receive the data. Try the following:
<?php
$track = "spotify:track:5ChkMS8OtdzJeqyybCc9R5";
$url = "https://embed.spotify.com/oembed/?url=".$track."&format=json";
$ch = curl_init();
curl_setopt($ch, CURLOPT_URL, $url);
curl_setopt($ch, CURLOPT_RETURNTRANSFER, 1);
curl_setopt($ch, CURLOPT_USERAGENT, "Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US; rv:x.x.x) Gecko/20041107 Firefox/x.x");
$output = curl_exec($ch);
curl_close($ch);
$get_json = json_decode($output);
$cover = $get_json->thumbnail_url;
echo $cover;
Using CURL allows you to be more granular with your request. In this example we are setting a User Agent.