Based on the generic example doc.
Github has not a discovery url. It's using OAUTH2 and not OpenId connect.
You have to set manually the configurations to access to the user informations.
<?php
require dirname(__FILE__, 2) . '/vendor/autoload.php';
$client_id = 'yourClient_id';
$session_key = 'YWQ4Q1Hpb_zQliS5wGYDDPZm2xC7PzyfjgLKBNodkazkN_pEPlm7yVBw5r9_pDzSwHJRsFVZShQyb_LFUSMBGQ';
$callback_url = 'https://yourAPPurl/callback.php';
$client = new Svgta\OidcClient\init();
$client->setSessionKey($session_key);
$client->client_id($client_id);
$client->add_OP_info('authorization_endpoint', 'https://github.com/login/oauth/authorize');
$auth = $client->authorization($callback_url);
$auth->set_state();
$auth->exec();
<?php
require dirname(__FILE__, 2) . '/vendor/autoload.php';
$client_id = 'yourClient_id';
$client_secret = 'yourClient_secret';
$session_key = 'YWQ4Q1Hpb_zQliS5wGYDDPZm2xC7PzyfjgLKBNodkazkN_pEPlm7yVBw5r9_pDzSwHJRsFVZShQyb_LFUSMBGQ';
$client = new Svgta\OidcClient\init();
$client->setSessionKey($session_key);
$client->client_id($client_id);
$client->client_secret($client_secret);
$client->add_OP_info('token_endpoint', 'https://github.com/login/oauth/access_token');
$client->add_OP_info('userinfo_endpoint', 'https://api.github.com/user');
$tokenRes = $client->token();
$tokens = $tokenRes->get_tokens();
$userInfo = $client->userInfo();