I believe I have been misunderstood. I have a different color and white light, which functions properly, which makes me believe it's a problem with the light rather than a Matter protocol limitation. Here is what happens: the screenshot below shows the Smart Life state, which shows the cool white color (which is the actual state of the light). The Matter is showing that the light is green, while it should be cool white as well:
Here is the Matter state, the light is green instead of cool white:
Looking at the Matter cluster states, the light is reporting ColorMode value 0 of ColorControl Cluster, when I believe it should be 2 for the white temperature:
Here is an example of a different light, connected to the same gateway, set to the same cool white setting:
The Matter is showing the cold white (the actual state of the light) and not color, as it should. The ColorMode state is 2.
The new virtual ID of the broken light (after re-pairing it): bf7abdc675304cc8747oxn
The virtual ID of the different working light: bfcac466d7df7a7161blyq