Hi Daniel
My overarching thought about pranayama is that it can be dangerous. Treat with caution! Having said that, there are pranayama practices and pranayama practices. Soft, quiet pranayama like Ocean Breath (aka ujjayi), is quite benign as is
nadi shodhana (aka alternate nostril breathing) as long as it is not taken to extremes (don't do it more than 3~5 minutes at a time). But the more vigorous practices like
kapalabhati and bhastrika will affect your blood chemistry and its PH balance and have the potential to make you quite sick. If you are going to do those, do so under the close guidance of a teacher who is experienced in advanced pranayama techniques. Those advanced practices are done separately from asana or meditation. I mention the practice of pranayama a bit in my books and you can see the YinSight discussion
here.
The separate pranayama sessions are not mindfulness practices per se: they are practices designed to deliberately change your state of consciousness through affecting the breath. When you do this, your breathing will generate a deficit of carbon dioxide. When that happens, the body will stop breathing in order to rebuild the CO2 levels in your blood, and those moments between breaths are the moments between thoughts. That is the intention...the stilling of the mind, so you can achieve states of samadhi. But, again, that is playing with dynamite as you are drastically altering blood chemistry and if you are not prepared properly, this can damage your brain and other organs.
In yin yoga, we don't do the dynamic, yang breathing practices: our intention is not to achieve samadhi. Instead, see this
article on the yinside of breathing. Here I say “A slow ocean breath while you are holding your Yin Yoga poses will reduce stress, active your rest & digest system, improve your heart and lungs function, lower blood pressure and lead towards a healthier and happier life., I would do the Ocean Breathing for maybe one pose near the beginning of the practice, but then let the breath find its own level after that. I would not suggest doing any pranayama while in shavasana: that is the time to die! No effort. Let it all just be. And, that is very yin.
Cheers
Bernie