I watch my kid's lessons and I'm sure I didn't see it being shown to them. They got into what I google as "backstroke" straight away, without the "elementary" phase.
I don't think I was ever taught it. I think I just discovered it playing around in the water one day.
When I want to play around, I try swimming backwards. On my back, with my feet straight ahead and motionless, I stroke backwards with my arms so I move in the direction my feet are pointing.
They never taught the “Elementary Backstroke” to us, even though this was Wilmington, NC and we were just fifteen minutes from the beach.
The backstroke I learned was more like the crawl, just done on your back. After a while, I stopped bothering to use my arms and did a lazy backstroke using just my legs. I could do that for hours on end. The lazy backstroke wasn’t YWCA approved, but it worked well in the ocean and in pools. The only danger was that you couldn’t see what you might be about to hit.