I just checked and the cookie is actually redesign_optout. The value doesn't seem to matter - I just checked with value xyz and it worked.

Here's the bookmarklet I use:

javascript:(function(){const old_or_new = prompt("[O]ld or [N]ew?", "New");if (old_or_new.charAt(0).toUpperCase() == 'N') {document.cookie = 'redesign_optout=; Path=/; Domain=.reddit.com; Expires=Thu, 01 Jan 1970 00:00:01 GMT;';} else {document.cookie = 'redesign_optout=true; Path=/; Domain=.reddit.com';}window.location.reload()})();