based only on my memory, when computers started to get small enough to have power switches that I had access to, the power toggle switches were marked with 0 and 1, and no other appliances had that, so it was basically engineers of digital devices marking things with some combination of obvious logic and humor.
the on-off-merged-in-one-pushbutton 0 with a 1 at 12 oclock (in the circle of the 0) came later, I assume out of Europe (Asia?), because suddenly all at once everything had them, mid 90s I think. That was also the beginning of globalization (meaning, identical products sold everywhere) and also "on/off are advisories, not switches", which was probably all just coincidental timing.
(I don't think the 0/1 toggle computer power switch labelling somehow had more influence over Europeans or Asians than it did over Americans, but I dunno, engineers are pretty universal)
Your memory is serving you very ill. These various symbols were standardized in 1973. The one that you are searching for a name for is the standby symbol. Standby buttons do not actually power computers off. (Circuitry that handles waking up from standby is, of course, still powered on.)
I was really struggling to figure out what symbol you were talking about and I couldn't come up with anything. Looked it up and __you mean the power_ icon! I never considered it was made up of the 1 and 0 used for on/off states.
Was that the case when the PlayStation initially released?