For our hosted version, the session runs in our hosted browser. For the open source, it runs on a local browser.
In the hosted version, users can choose to pass logins at runtime or store them in our vault. Once a user logs in, we keep their session as a Chrome profile and attach it to a sticky IP, so that they stay logged in for longer.
Deterministic tools return only the structured fields, and don't parse the whole browser DOM. Since tools are deterministic, we also reduce the risk of prompt injections.