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?
So, it’s basically a loss leader in this scenario to feed other sevices like the ad network?
For personal Gmail yes.
Yes. About 75% of Google’s revenue is from ads. Most (all?) of their free products exist to feed the advertising business in one way or another.