Rate limits despite paid plan

Hi,

I have a google cloud project with enabled billing (2 credit cards and 1 paypal account). For this project I have created an API key in the Google AI Studio. It says paid tier. However I am still running in the free tier limits. I have already consulted Billing  |  Gemini API  |  Google AI for Developers, but as always with Google documenation, it is faulty, outdated and misleading.

Please help me give you my money.

Cheers,
Justus