It's relatively straightforward. You open the console, type window.localStorage, and poke around. On the article I see:

    > window.localStorage
    Storage {dark-mode-toggle: 'light', cid: '2722...', length: 2}

Ignore the "length" (implementation detail) and you can see it's storing whether I've turned on dark mode and some id that's likely per-user. If I switch the page to dark mode I see instead:

    > window.localStorage
    Storage {dark-mode-toggle: 'dark', cid: '2722...', length: 2}