All that has changed is the line:
$result = file_get_contents_utf8("https://discordapp.com/api/channels/" . $channel . "/messages?token=" . $token);
has been changed to:
$result = file_get_contents_utf8("https://discordapp.com/api/channels/" . $channel . "/messages?token=Bot%20" . $token);
due to the fact that the Discord API now requries the word "Bot" before providing the key in requests.
There are redirection PHP scripts to redirect Garry's Mod GET and POST requests to the Discord API. CloudFlare that uses Discord do not allows GMod browser to send GET and POST requests that is the reason you must use redirection. Just upload this files to your web-server and configure api links at /lua/autorun/server/discord.lua