Context: I am visiting a high school friend. Another friend who we both knew in high school has posted some interesting things recently. This friend has changed their name, but the friend I am visiting is not following them and is not aware of their transition.
How do I bring up this friend without dead naming them?
I agree with the person who said it's generally okay to use the dead name in this particular situation. Either by waiting until the friend you're visiting uses the dead name or by bringing it up yourself with something like "Our friend formerly known as [dead name] is now [new name]". Just try to do it in a private situation and not, like, in a situation where you're in front of a bunch of the friend's coworkers/friends who only know them by the new name.
Or, if you really want to avoid that anyway, you could refer to them in a roundabout way by a recognizable hobby or job or aspect of their appearance, like: "our friend the photographer is now [new name]" or "our friend with the yellow jacket is now [new name]" or similar.
I guarantee you it'd also be safe to ask (if you want to) the mutual friend themself how they'd prefer you do it. They're very unlikely to be offended by a question like that, and it might even make them happy because your asking shows that you're thinking about things like this and respecting their new pronouns/name even when they aren't there.