AI Studio uses your API account behind the scenes, and it is subject to normal API limits. When you signup for AI Studio, it creates a Google Cloud free tier project with "gen-lang-client-" prefix behind the scenes. You can link a billing account at the bottom of the "get an api key page".

Also note that AI studio via default free tier API access doesn't seem to fall within "commercial use" in Google's terms of service, which would mean that your prompts can be reviewed by humans and used for training. All info AFAIK.