I don’t know what is going on. It would be good to know more about you. You are unique: your life story is uniquely yours (your biography); your anatomy, physiology, current conditions, etc. are also unique to you (your biology). Without understanding your biology and biography, there is no way I can really know what is going on. I would also wonder about things like: has this happened to you before? What else is going on with you right now? Are you mentally/emotionally in a good place or are there other stresses in your life right now? How has your sleep been? Diet okay or has it recently changed? Are you taking any supplements or prescriptions that may have changed? And, many other things along these line (menopause, period, recent illnesses, relationships, job, did you move…)
I could speculate … but please accept these only as wild guesses that are totally uninformed by knowing you.
Maybe it is an imbalance between the sympathetic nervous system (SNS — our waking up/fight or flight system) and the parasympathetic nervous system (PNS — our rest and digest system.) We need both to be active at appropriate times, but it is possible that Yin Yoga turns off your SNS so well that you are left in a PNS state for a long time afterwards. It may be possible to re-activate the SNS at the end of your Yin Yoga practice, even after your final shavasana. Various techniques can include breathing through the right nostril for a couple of minutes (close your left nostril with a finger), powerful pranayama practice for a few minutes or chanting/singing (but please be careful: don’t over do this), some yang asana practice like the Golden Seed
for a few minutes, or a nice cup of jasmine tea or a square of dark chocolate (something with a little bit of caffeine).
Given your experiences, I would also suggest skipping your Yin Yoga practice for a while (a week or two) and then re-introduce it slowly: maybe once a week for 30 minutes at a time. See how that goes. If you find that you still experience this ongoing lethargy even when you are not doing yin, then it is time to check-in with your health care team. There may be more going on than you realize and it may have nothing to do with your yin practice.