I realise that Google places ads in the native Gmail environment. However, when using a third party front end to embed the Google services, how does the company make money off that? When I use Thunderbird to access Gmail or the Google Calendar or when I map my Google Drive to the file explorer, how can Google profit from this kind of use?
They probably make more money selling data collected from its use through any means, than they do selling ads in their own apps.
Remember: If the thing is free, you are the actual product getting sold.