So Claude seems to have access to a tool to evaluate JS on the webpage, using the Chrome debugger.
However, don't worry about the security of this! There is a comprehensive set of regexes to prevent secrets from being exfiltrated.
const r = [/password/i, /token/i, /secret/i, /api[_-]?key/i, /auth/i, /credential/i, /private[_-]?key/i, /access[_-]?key/i, /bearer/i, /oauth/i, /session/i];
replies(3):