Matching Inovelli Blue Switch LED Color with LED Bulbs?

I have a room full of RGB LED bulbs and the Bulbs get a Random Color every time we enter. All bulbs get the same color. I'd like to have the LED on the Switch change to that same color as well. I don't seem to have the ability to create a child device on these switches like I could with the old generation which would have made this easier. I know I can use RM with a custom action to change the color but how would I ever match it with the rest of the room?

Could the random color be anything, or is it limited to basic colors?

I think you'd need to capture the bulbs' color as a Variable value and then figure out a way to convert value that into the methodology Inovelli uses to code their colors. That may be easier if limited to basic colors, but could get complicated if any color is a possibility.

I've never used a Variable value in any of my "ledEffect..." custom actions, but based on a cursory glance at such options, that seems like it should be possible.

I use Rule Manager to set color to random so I think it can be any color. Might not be worth the effort for such a small gain. I was hoping for a simple solution but sounds like there may not be a simple one.