I have amblyopia—also known as lazy eye—which means I often see a bit of double vision—usually a sliver duplicated on the outside side of one of my eyes, even when I’m wearing contacts, and even though I don’t look like I have a lazy eye. My eyes definitely don’t work in concert and I’m told my 3D vision resembles what people see when they look at a postcard.
Finally, when I use binoculars, I use only one eyehole up to the non-lazy eye… So I’m wondering what exactly you normal people see out of binoculars? Is it like Looney Tunes?
Until you get them adjusted, you can get this kind of view (sort of), especially when you first pick them up and are bringing them to your eyes.
Once situated correctly (with the rubber eye cups touching your face so the lenses are the same distance away), your brain merges the images just like wearing glasses.
You can get this effect if the binoculars haven't been adjusted to match your pupillary distance (how far apart your pupils are).
For film purposes though, it's an excellent way to keep the image filling most of the screen and to communicate the subtle contextual implications of the character's using binoculars rather than a telescope.
But binoculars have an adjustment that brings the view through the two scopes together. If you see two circles (or two overlapping circles), you should adjust it.
I had amblyopia as a kid because one of my eye muscles didn't develop properly, so there was an imbalance leading to a lazy eye. I had to get surgery to correct that, but it was past the time window when proper depth perception is developed (until about 7 years of age, got my surgery with 9). So yeah, my vision is kinda like yours.
Even with the lazy eye gone, I also only use my stronger eye to look through binoculars, dunno why. But I'm myopic in the right eye and hyperopic in the left, so maybe that has something to do with it.
I gather you have never actually used a binocular. In reality, a good binocular has a wide FOV that you barely notice a border on the peripheral vision. At worst, you see a single circle around your vision, not two overlapping circles, that's just Hollywood shorthand, not something that happens in real life.