I don't know about how the brain is wired, but from a simple optics/geometry perspective, I think we can reason that your "tied 1:1 ..." suggestion is unlikely.

In any given scene, the two eyes don't see exactly the same thing, owing to the different viewpoints. We experience "stereo-disparity", and the principal effect of that is that the relative horizontal alignment (in the two eye) of different points in the scene depends on their depth.

I would argue (I can't prove) that we perceive a range of depths "instantaneously" without having to scan the eye-divergence to bring each conceivable depth into alignment (to meet some 1:1 mapping).

Similarly, if you were to look off-axis (like 30 degrees to the left or right) at something quite close (e.g. 20 cm away), the images will be noticeably different sizes on the two retinas (provable from basic geometry), so again a "1:1 mapping" isn't helpful - and in reality we can still fuse a 3D image in the brain.

I've spent a lot of time in the past creating 3D autostereograms and thinking about stereoscopic depth perception - and depth reconstruction from an image-pair. It's not trivial.

At some level the brain must be 'correlating' the two images with a range of possible horizontal-offsets (dependent on relative depth), and some small finite vertical tolerance too (to allow for optical distortions and misalignments). I think I read about tests (or maybe did my own tests 20+ years ago) showing that the human brain can stereo-fuse (and perceive different depths) even if the image presented to the left and right differ in size/magnification by up to about 10%.

Also this video is quite interesting https://www.youtube.com/watch?v=DkaJ6iK2CJc The ability to barrel-roll the eye (to a limited extent) is likely part of human "optical image stabilisation" !