> I am baffled by this. Not only, because I use the online website (= I am not using the API, like in a terminal)
Why would this baffle you? API's are typically accessed programmatically, so there would be no human to solve the captchas.
> I am logged in and a paying customer. Why am I getting asked if I am human?
To prove that it's a Human accessing the interface and not a robot.