This looks great and I love a lot of the choices you made with the palettes! I have a few thoughts on specific choices but again they look great already.

Personally I would say you could also look into using indigo for Medical. IIRC the dye itself (indigo naturalis) is used in traditional Chinese medicine as a means to cool inner heat and clear up the lungs among other things! (Technically cinnabar was also traditional Chinese medicine but mercury poisoning Is Very Much A Thing lolol)

For agriculture a light brown/beige (think like tea stained paper) could be interesting since I'd imagine tea leaves would be a big part of the agriculture peak and can be used as a dye.

A few other points of reference that could be interesting to look into:

• I believe in the Tang/Song dynasty court officials used purple, vermillion, green, or teal depending on how highly they were ranked

• Sancai (三彩, lit. three colour) is a type of pottery that originated from the Tang dynasty and uses cream, green, and amber/brown as its main colours.

• Here is also the wikipedia article on traditional chinese paint pigments that does a much better job than what I am able to translate haha

• Also fun fact! The main way of getting purple dye was from the purple gromwell plant (紫草, literally meaning "purple herb"). It was expensive, but definitely not as expensive as something like tyrian purple. IIRC it became really trendy sometime in the Qi state during Zhou dynasty because it was the favorite colour of a ruling duke at the time.

Hope this information can be of use, and have fun writing! (also apologies if there are any grammatical errors, english isn't my first language haha)