I’m pretty sure the info submitted through Studio and any free part of the Developer API is subject to use by Google.
From Gemini API Additional Terms of Service | Google AI for Developers
“How Google Uses Your Data
When you use Unpaid Services, including, for example, Google AI Studio and the unpaid quota on Gemini API, Google uses the content you submit to the Services and any generated responses to provide, improve, and develop Google products and services and machine learning technologies, including Google’s enterprise features, products, and services, consistent with our Privacy Policy.”