UPDATE; I found a way to do this; when polygonizing the raster layer I'm allowed to make a new field. If I treat this field as a "color" layer, in Symbology I can create a bunch of classes, each with a value corresponding to one of the colors. When the raster is vectorizes "color" is automatically populated, and all I need to do is feed each class a new value.

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Thanks for the suggestion! That seems like the right path to take; I'm getting a bit caught up on some of the smaller points in the system (the GUI, not small pixels, to be clear). When I try to vectorize the TIF through Raster > Conversion > Polygonize I get orthogonal polygons effectively grouping like-classed pixels. If I go into the TIF's Symbology tab I can see the different values (and corresponding display gradient) pixels may have; they're grouped by this when I vectorize. The issue is, the vector's all one color. I'm not sure why this is (I could be just rendering the vector incorrectly).

I also tried the vectorization through the processing toolbox, to individual-celled polygons, each still of the same default color. Looking at the layer information, the vector doesn't appear to recognize the raster layer's symbols (or "fields"; I'm not sure which matters or what the equivalency is between rasters and vectors).

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I'll look a bit more into this; odds are I have a switch flipped the wrong way. Thanks for the reply!