The case is not a piece of cake because nobody here knows what you actually have there - maybe combined paths, groups, effects, photographed drawings or anything. You have succesfully hidden all essential data of your object structures.
The case would be a piece of cake if your shapes were simple like this:
In the left there's my number 8. It contains 4 separate closed curves which do not have any groups nor effects, only plain thin black strokes with no fill. The parts are moved apart in the right only to show they are independent. I left out 2 curves of the inner white area to keep this simple.
In the next screenshot the number is selected and the Shape Builder is just used to mark the 2 areas between the curves which should be separately colorizable objects:
If I guess right the shape builder is the closest really existing thing you wanted, but still haven't found. To fill areas between the curves there's available also the paint bucket, but its not useful for subpixel accurate work.
In the next image the outer shape has got yellow fill (white is not visible on white background) and the inner shape has got red fill. Just to show them separately the parts are moved apart in the right.
The black strokes are still there. They can be removed. But it's useful to have a thin red stroke for the inner shape, because Inkscape's rendering would otherwise leave a 1 pixel wide partially transparent gap between the inner and the outer shape. It could be seen if there was something bright or dark behind.
As I said, I left intentionally 2 curves out. But in theory they are not needed. Only click with the shape builder also the holes. Do not fill the generated shapes, but give a wide stroke. Of course, there's less control over the actual form of the colored area.
The shape builder is available in Inkscape version 1.3. It's only a subset of the shape builder implementation in Illustrator, but it's still handy when compared to making path combination operations.
About the paint bucket: It can also used to generate filled areas between curves or otherwise differently colored areas. It works only in screen resolution. Essentially it's bitmap tracing of the rendered image on the screen. It's useful only in cases where the inaccuracy is no problem.