Does gerd/acid reflux always cause stimulation of the vagus nerve? If yes, are symptoms of stimulation different from those of anxiety?

Vagus. Interesting question. Symptoms of stimulation of the vagus nerve are not usually associated with anxiety. The vagus nerve has many functions and I won't go into all of them here do to space limitations. Reflux can cause stimulation of the nerve and chest pain and synocope/near synocpe (passing out) can happen but that's often in severe cases and usually with cold/hot beverages/drinks.
No. It can stimulate the vagus but that is not common. Many times anxiety can feel like heartburn but it should be relatively easy to tell the difference because ppi drugs like Prilosec otc won't help anxiety chest pain but they will help chest pain from reflux.