The site works without advertising trackers, analytics profiles, or third-party advertising cookies. A generator request is a single form submission, and the page does not need a persistent identifier to show the result.
A browser may keep ordinary cache files for the stylesheet, the script, and the icons so the site loads faster on a second visit. These are technical files served by the site itself. They are not used to build a profile of a visitor.
There is no login, no session cookie, no advertising identifier, and no cross-site tracking pixel. The context line you type is sent with the request to produce a result and is not written into a cookie or a local profile.
The text generation call is made to a service provider on the server side. That provider receives the prompt needed to answer the request. It does not receive browser cookies from this site, because the browser never contacts it directly.
You can clear the cache and site data in your browser at any time. Doing so will not remove any account or saved list, because neither exists. Blocking storage entirely should not stop a generator from working.