The VG Resource

I am ripping some Sonic Mania stage models, and I am confused at how to color the vertices correctly. I already have converted the models to both STL and OBJ formats, yet they appear colorless.

None of those format supports vertex colors (at least in their standard implementation).

You'd need FBX for example, or PLY, which is the simplest format that still manages vertex colors that I know of, nice if you're writing your exporter yourself (Blender imports/exports natively PLY files).