My client has a specific requirement that any colors used in a texture are their listed approved colors. Is there a way to generate a "report" of what colors have been used on the base color layer? Can I export a list of HEX codes / color swatch / or something similar that I can supply to client to verify that we have only used approved colors?
I'm afraid I'm not going to be too helpful here, but I recommend pushing back against this requirement if at all possible. Color spaces are going to make this a very complicated question (do they want you to use that color in RAW format, or in sRGB? Does that color even exist in sRGB?), in addition to reflectance values and metalness having an effect on the final output.
With dithering and anti-ailiasing, that auto generated report would also contain a lot of gradient values that do not meet your clients requirements. You could take it into PS and show the client the histogram or something like that to show the prevailing colors... Or best option if you can't shut down that request would be setting opencolorio to RAW and using the color picker, taking screenshots and sending them to the client. It's not going to be scientific, and it's not really going to be right, but if they just need to check off a box, that might do it.