Yes, I do the same. Or I did at least, since as you I tried to be more conscious about my posture. And I did some Yoga years ago, which helped a lot.
In addition I have a slightly strange walking style. When watching me from the side, I do something wrong with my legs. Can't tell for sure, what exactly. I think it's that I somehow more fall forward than really walking But that too disappeared mostly, when I started to walk more upright.
I'm not sure why I do/did this. Maybe it's just I'm born that way.
Maybe I took my parents to literal, when they told me to watch where I walk.
But most likely it's just to avoid eye contact by looking down on the street all the time.
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Deep into that darkness peering, long I stood there wondering, fearing,
Doubting, dreaming dreams no mortal ever dared to dream before (E.A.Poe)