I took another look at the problem at different angles. My computer is incredibly under-powered – likely more so than yours, so there was a lot of waiting for the CPU/GPU to catch up and screen to refresh.
I tried saving the SVG and opening it again. I get
I also tried exporting the bitmap and traced object, respectively, using “Export PNG Image”. Takeaways:
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On my system, exporting doesn’t remove the color shift. Since I don’t trust my eyes, I used a global system color picker to verify. Note the overlaid purple rectangle: I measured the top-left and bottom-right patches inside, comparing raster and vector in app and their exported versions.
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The color shift isn’t uniform, which makes me suspect that it has to do with issues related to not only posterization but color conversion and management.
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As @D_Gowers mentioned, Inkscape’s trace tool is based on Potrace. Have you tried using the tool directly? As-is, I don’t believe that Potrace is meant to trace color images.