I don't know if what I think I've found would be called, "mindful posture/posturing"; I think that that has to do with Buddhists' notions of meditation.
The thing I found is mindfully seeking the proper alignment of my upper torso, legs, and soles of my feet in the most balanced and relaxed form as I stand still. I also seek the most relaxed, balanced gait as I walk.
This has been kind of a switch for me because I've always slouched sitting and standing, and, now, I've developed an arthritic right hip and a sometimes audible, clicking pop of my right knee cap if I have sat for too long and then I move to stand up.
I think this intention of mind and body in the way I stand and walk not only helps with the way I sit, but also that it helps me with my overall sense of well-being. I seem to be more awake and engaged.