Youtube Data PHP API - Service Error "Invalid Credentials" - php

Question

I want to upload a video on YouTube via php. To do this, I've followed this tutorial to get the rights (authenticate) and this to upload the video.
The authentication works as it should. The user is redirected to a google site, accepts that I have a right upload YouTube videos, etc. and is redirected to my site again. There, the access token is saved.
But if I want to upload a video, I get this error:
A service error occurred: { "error": { "errors": [ { "domain": "global", "reason": "authError", "message": "Invalid Credentials", "locationType": "header", "location": "Authorization" } ], "code": 401, "message": "Invalid Credentials" } }
To test my application, I've tried to retrieve my uploads instead of uploading a video, but the same error occurred.
I have no idea what triggers this error.
Here is my code from the site which redirects the user to google:
$OAUTH2_CLIENT_ID = "Not on Stackoverflow (but here is a code)";
$OAUTH2_CLIENT_SECRET = "Also not on Stackoverflow";
$client = new Google_Client();
$client->setClientId($OAUTH2_CLIENT_ID);
$client->setClientSecret($OAUTH2_CLIENT_SECRET);
$client->addScope("https://www.googleapis.com/auth/youtube.upload");
$client->addScope("https://www.googleapis.com/auth/youtube");
$client->setRedirectUri("my site(actual link)");
$client->setAccessType('offline'); // offline access
$client->setIncludeGrantedScopes(true); // incremental auth
$auth_url = $client->createAuthUrl();
echo 'Allow posting on YouTube (click)';
Here is my code from the site the user is redirected to from Google:
$OAUTH2_CLIENT_ID = "Not on Stackoverflow (but here is a code)";
$OAUTH2_CLIENT_SECRET = "Also not on Stackoverflow";
$client = new Google_Client();
$client->setClientId($OAUTH2_CLIENT_ID);
$client->setClientSecret($OAUTH2_CLIENT_SECRET);
$client->addScope("https://www.googleapis.com/auth/youtube.upload");
$client->addScope("https://www.googleapis.com/auth/youtube");
$client->setRedirectUri("my site (actual link)");
$client->setAccessType('offline'); // offline access
$client->setIncludeGrantedScopes(true); // incremental auth
$client->authenticate($_GET['code']);
$access_token = $client->getAccessToken();
//Acces token is being saved
And here is the upload code (which doesn't work):
$OAUTH2_CLIENT_ID = "--";
$OAUTH2_CLIENT_SECRET = "--";
$client = new Google_Client();
$client->setClientId($OAUTH2_CLIENT_ID);
$client->setClientSecret($OAUTH2_CLIENT_SECRET);
$client->addScope("https://www.googleapis.com/auth/youtube.upload");
$client->addScope("https://www.googleapis.com/auth/youtube");
$client->setRedirectUri("https://www.socialme.online/YoutubeFT.php");
$client->setAccessType('offline'); // offline access
$client->setIncludeGrantedScopes(true); // incremental auth
$client->setAccessToken($access_token);
$youtube = new Google_Service_YouTube($client);
try {
$snippet = new Google_Service_YouTube_VideoSnippet();
$snippet->setTitle($Titel);
$snippet->setDescription($Beschreibung);
$snippet->setTags(array("tag1", "tag2"));
$snippet->setCategoryId("22");
$status = new Google_Service_YouTube_VideoStatus();
$status->privacyStatus = "public";
$video = new Google_Service_YouTube_Video();
$video->setSnippet($snippet);
$video->setStatus($status);
$chunkSizeBytes = 1048576;
$client->setDefer(true);
$insertRequest = $youtube->videos->insert("status,snippet", $video);
$media = new Google_Http_MediaFileUpload(
$client,
$insertRequest,
'video/'.$extension,
null,
true,
$chunkSizeBytes
);
$media->setFileSize(filesize($new_path));
// Read the media file and upload it chunk by chunk.
$status = false;
$handle = fopen($new_path, "rb");
while (!$status && !feof($handle)) {
$chunk = fread($handle, $chunkSizeBytes);
$status = $media->nextChunk($chunk);
}
fclose($handle);
$client->setDefer(false);
} catch (Google_Service_Exception $e) {
$htmlBody .= sprintf('<p>A service error occurred: <code>%s</code></p>',
htmlspecialchars($e->getMessage()));
} catch (Google_Exception $e) {
$htmlBody .= sprintf('<p>An client error occurred: <code>%s</code></p>',
htmlspecialchars($e->getMessage()));
}
echo $htmlBody;
I've no idea what causes this error, especially as most code is taken from the official Google documents. The URL in redirect_uri is valid and the same as the one, authorised in the Google Console. The link to the video is valid, too.
Thank you for your help.