Hi Matthew I have a similar situation but at a book level.
I have a master template for a set of study guides for various subjects, with each subject having a theme colour. I have colour swatches for each subject plus a ‘base’ swatch that is used in the paragraph, character and object styles in the master template file.
When I create a new book, the title chapter is my sync master for the book, which gets synced from the template. I then merge the base and subject swatch, retaining the subject colour swatch which then updates in all the styles. What this means is that if I ever have to resync a book because my template styles have changed, I do have to repeat the swatch merge in the book master because all the paragraph etc styles will have been synced back to ‘base’. So, the sync cascade for me is book master template > book chapter master > all chapters. Generally, I only have to do this merge once for each book as my template styles are fairly well established.
In your context, you could define a swatch for each chapter colour, in your sync master chapter you already have your base ‘CHAPTER COLOUR’ colour swatch baked into your styles and formatting, and then sync all styles as normal to the other chapters. In each chapter file you would then merge ‘ CHAPTER COLOUR’ with the relevant chapter colour swatch (retaining the ‘chapter’ swatch) which will update all the colours in that chapter.
If you are actively developing your styles in the template, then as you have to merge after every sync you could just leave the swatch merge until the end of the process. To avoid forgetting to do that I make the ‘base’ swatch a really obvious colour, although another thing you can do to be sure is define your base colour using a colour space you aren’t using (e.g. Lab or HSL) and then add the colour space as not allowed in your Pre-flight check profile.
In the absence of having a variable that can set these things you have to accept some part of the process is manual. I saw a script in the link David included and this may work for you but while I like scripts for repetitive or more complex tasks, in this case I would find running the script just as manual as selecting two swatches and right-clicking to merge them. The advantages I find in my approach are that my styles are all consistent for sync, I don’t have the same colour swatch representing different colours across files, and I can easily update or add to the subject colours in future without changing the workflow (or having the check/update a script).