This is potentially doable but a little tricky. At the moment, we haven’t added dark mode auto switching to the embedded comments endpoint. We can add that, and it would work if your Ghost site was auto-switching to dark mode when the browser switches to dark mode. But from what I can tell, your Ghost site uses a dark mode button, which won’t work with the Discourse implementation.
What you can do in your specific case, is toggle a class in the Discourse embedded comments iframe when clicking the button, and then use that class to toggle colors in your embedded stylesheet.