Try putting your .icc profiles in ~/.config/Cyan/icc mine looks like this.
FWIW I also have profiles in /usr/share/color/icc/colord/
Might be a good idea while there to delete ~/.config/Cyan/Cyan.conf and start "as-new" like this: https://i.imgur.com/47zWXnj.mp4
Export an image goes like this: https://imgur.com/AwpzA2N.mp4
Open a CMYK image goes like this: https://i.imgur.com/njbVo2E.mp4
FWIW I also have profiles in /usr/share/color/icc/colord/
Might be a good idea while there to delete ~/.config/Cyan/Cyan.conf and start "as-new" like this: https://i.imgur.com/47zWXnj.mp4
Export an image goes like this: https://imgur.com/AwpzA2N.mp4
Open a CMYK image goes like this: https://i.imgur.com/njbVo2E.mp4