I think so, yes. Musk could be held responsible for wider matters, I guess, matters of corporate policy, or a failure to act after the event, but on a platform such as X individual posts have got to be down to the person who posted it, at least as the law stands as I understand it.
I think social media should be regulated far more stringently, but that is a separate point.
There's a pretty easy conclusion here. Twitter started as a "micro-blogging" site. Tweets were just short blog posts.
If Barton had posted these comments to his personal blog at www.joeybarton.com no one would question his own liability for his words.