nodsocket When you say visiting a website through an app, that sounds like a custom tab in Vanadium, and not the WebView browser.
A custom tab looks a bit like a normal Vanadium webpage, but rather than the address bar at the top you will see a different bar, with an X on the top left to close, and 3 dots context menu on the top right.
If it is a custom tab, the cookies and site data are saved within Vanadium. You can view and delete the cookies and site data, from Vanadium > Settings > Site settings > Data stored.
If you really are browsing using the WebView browser, then you would most likely need to clear the user data of the app, to clear any cookies and site data saved.