Getting 403 Daily Limit for Unauthenticated Use Exceeded. Continued use requires signup. on YouTube API with already API Key

I’ve developed a WordPress plugin to pull videos from YouTube with the YouTube v3 API

The plugin works fine in most sites but currently I’m having an issue with one, I can’t seem to pass the error:

“Daily Limit for Unauthenticated Use Exceeded. Continued use requires signup.”

The weird thing is I can copy / paste the query with a valid API key on the browser and it works, I’ve tested with other Api Keys with the same results. It seems the problem is with that server

I’ve checked than other plugins were using the Google API, but disabled all of them and still getting the same error

I don’t know what to do next

Here is an example of a basic query to the YouTube API

$request = new WP_Http;
$result = $request->request( 
    'https://www.googleapis.com/youtube/v3/channels?part=id&forUsername=USERNAME&key=API_KEY', 
        array( 
            'method' => 'GET',
            'headers' => array('Accept' => 'application/json' )
        )  
);

The request is handled by the native WordPress class WP_Http