PHPmailer won't use SMTP - php

Question

I am using PHPMailer 6.2 (shared webhosting so I grabbed the latest version of the code from Github and uploaded it to my FTP. When I want to send mail without SMTP, there are no problems sending mail. When I do use SMTP (and I do need to), however, nothing happens. It kind of looks like the page won't load at all. I don't get errors or notices, so I'm at a loss what I'm doing wrong here. Using an SMTP test tool, I see that my credentials and the connection details are OK. Here's my code:
<?php
ini_set('display_errors', 1);
ini_set('display_startup_errors', 1);
error_reporting(E_ALL);
use PHPMailer\PHPMailer\PHPMailer;
use PHPMailer\PHPMailer\Exception;
require __DIR__.'/PHPMailer/src/Exception.php';
require __DIR__.'/PHPMailer/src/PHPMailer.php';
require __DIR__.'/PHPMailer/src/SMTP.php';
$mail = new PHPMailer(TRUE);
try {
$mail->setFrom("xxx", "Test");
$mail->addAddress('xxx', 'Test');
$mail->Subject = 'Bericht via de website';
$mail->Body = "hier een testbericht";
$mail->isSMTP();
$mail->SMTPDebug = 1;
$mail->Host = 'smtp.gmail.com';
$mail->SMTPAuth = TRUE;
$mail->SMTPSecure = 'tls';
$mail->Username = 'xxx';
$mail->Password = 'xxx';
$mail->Port = 587;
$mail->send();
} catch (Exception $e) {
echo $e->errorMessage();
} catch (\Exception $e) {
echo $e->getMessage();
}
die("done");
?>
Edit: after 20 minutes of loading, the following response is generated:
2020-11-28 19:40:07 CLIENT -> SERVER: EHLO <my/e-mail rcpt domain>
2020-11-28 19:45:07 SERVER -> CLIENT:
2020-11-28 19:45:07 SMTP ERROR: EHLO command failed:
2020-11-28 19:45:07 CLIENT -> SERVER: HELO <my/e-mail rcpt domain>
2020-11-28 19:50:07 SERVER -> CLIENT:
2020-11-28 19:50:07 SMTP ERROR: HELO command failed:
2020-11-28 19:50:07 CLIENT -> SERVER: STARTTLS
2020-11-28 19:55:07 SERVER -> CLIENT:
2020-11-28 19:55:07 SMTP ERROR: STARTTLS command failed:
SMTP Error: Could not connect to SMTP host.
2020-11-28 19:55:07 CLIENT -> SERVER: QUIT
2020-11-28 20:00:07 SERVER -> CLIENT:
2020-11-28 20:00:07 SMTP ERROR: QUIT command failed:
SMTP Error: Could not connect to SMTP host.
SMTP Error: Could not connect to SMTP host.```