First, no, anxiety is not in your body. Fear, just like any other emotion is in your brain. You might get physiological responses in the form of chemicals in your body. That is an effect, not a cause.
Second, neocortex is not "thinking brain," its role is to manage social interactions. Cognition is a small part of that.
Third, mindfulness is the opposite of any therapy I can think of. It is an ego-depletion technique proven to be detrimental to people suffering from anxiety and depression.
Finally, I don't know who performed therapy on the author but some steps seem to be missing:
//> when you have an anxiety attack, the only thing you can do is to perform the grounding exercises. Yes, that is the moment you start counting and do square breathing exercises. If people in the military can do it while in stressful situations, you can do it from behind a macbook. Nothing is treated mid-episode.
//> once the episode is over, you can explore the trigger. Chances are that your response is healthy, you are in a situation you should be anxious, but your behavioural response is over the top. A trigger contains the stimulus, the circumstance and your personal patterns (e.g. personal experiences).
//> part of the role of the therapist is to help you figure out the patterns. The other is to see if your behavioural responses are productive for you or not. If loud sounds make you run like hell, that is a good thing in an active shooter situation or a war theatre. Not so much at a birthday party where a balloon popped.
/rant