Rather than showing the texts of colours (“red”, “blue”, “green” …) in a facet, why not show an image with the color as the background ?.
The idea is to associate colours to your field values, by picking a colour with a colour picker.
Choose the layout “Colour picker”

- Select the layout “Colour Picker”
- Open the facet values.
- Associate a colour with the colour picker. Do nothing if your value is already a colour, like “white”, or “#ffffff”.
This will generate the coloured facet :
