Edges of bottom layer's fills showing even with perfectly aligned shapes

L,

A very close look at the first screenshot reveals something strange at the corners of the faint/narrow line at the right which seems to have the cyan colour: it looks like separate open paths with Butt Ends, in other words something different to the dark rectangle and the three paths in the inner Group.

What is the object named Reserved, and what happens if you hide/delete it?

L,

This statement "If I have two identical & precisely overlapping shapes with different fills on top of each other," may be true, albeit only partially since only the right sides can be identical and precisley overlapping, but it would be nice to see both the white and the cyan (and preferably also the deep(er) blue selected and with Transform values shown with one of the right Reference Points ticked.

But whichever the issue, I believe you can mend it in the following way, working on a copy of the Group with the three paths, which you can hide and keep as back up, Smart Guides being your friends:

1) Lock the bottommost dark blue path,

2) Click an empty spot on the artboard, then with the Direct Seletion Tool ClickDrag over the two rightmost corners of the paths and press Delete; this ought to delete the straight segments of the white and cyan paths, leaving only the two curves to the left as open paths;

3) With the two open curves from 2) still selected hold Ctrl/Cmd and press X then F to copy them to the front, in other words above the dark blue path;

4) Deselect, then still with the Direct Selection Tool click each of the topmost end Anchor Points of the paths and ShiftClickDrag it a bit up and then down again to snap to the path beneath (Smart Guides say intersect), then do the opposite with the bottommost Anchor Point; this will ensure the two paths beyond the blue path;

5) Unlock the dark blue path from 1), then apply Pathfinder>Divide to have three closed paths in a Group, and then recolour.

Unknown to most, it is quite easy to directly show images in posts, hence the following general suggestion:

Please show images by using the Insert Photos button (looks like moon over mountains) for each at the top of the reply box which makes everything appear right there in your post together with your text, rather than he more conspicuous Drag&drop attachment which requires helpers to open a new tab for each image and wait for its showing, then go back and forth; and if they just click it and wait for its showing and press the X to get back to the text, the image is gone, so if they need another look they have to open it again and wait to see it again.