When the browser requests Kagi.com without JS and you navigate to the account section with the session link information (https://kagi.com/html/settings/user_details), the page doesn't reflect the lack of JS functionality. This means that users can click the copy button and nothing will ever happen since there is no JS to offer any feedback. Since the text field is greyed/dimmed, it gives off the air that you're not actually meant to interact with it (but you can!).
It would be nice if there was either a non-JS solution for the copy button to work (does HTML support this yet?), or hiding the copy button and making it more evident you can/should copy the text in the field manually if and only if no JS is available.