Has Peter Lakatos chimed in? He would be the a great resource here.
I’m a breathing instructor Buteyko and Ocygen Advantage and HeartMath. I love this topic and clarifying how we breathe and why.
Ultimately we want to breathe calm and how we breathe at rest is different than during activity. And not all activity it the same. The mouth should not be the primary breathing route squats, carries, running, get ups, etc. Also, the biomechanical breathing standard can be done with nasal breathing. It takes additional training of the diaphragm and respiratory system, and biochemistry to support it. But the Oxygen Advantage system does not single out and prohibit all mouth breathing, all the time. It depends on the person and the intent and goal of the training session.
Again I’d love to hear Peter’s perspective as he has great knowledge and experience in both breath work and StrongFirst. (Did he chime in?)