Google client library integration in codeigniter 4

Stop the Earth, I'll get off(с)

CI4 includes the Composer autoloader by default. 
This line is not needed.
require ROOTPATH . 'vendor/autoload.php'; 


The controller have App\Controller namespace.
When you create instance of the Google_client() , it is called in the App\Controller context.
But in this context, the Google_client class does not exist.

Read the library documentation how to create class instance. 

Read the php documentation about namespace.