This is an interesting question, although I'm wondering if it is even possible for HomeKit or Siri to specify a LED bulb color temperature since different manufacturer bulbs will have different capabilities and perhaps different ways to control the LED hue and color temp.
For example, Philips Hue has various types of bulbs - 'white' (fixed color temp, 2700K, referred to as 'soft white' or 'warm white); white ambiance (color temp controllable between 2200K-6500K, 'warm white' to 'cool daylight'); and finally white and color ambiance (color temp controllable between 2000K-6500K plus "16 million colors").
Homekit is a specification for how to transmit control info, so homekit is specifically designed to be able to specify a bulb color in a certain way, and then the device manufacturers program their devices so they know how to read the info. It doesn't matter how the bulbs talk to other things, when they talk to homekit, every device is talking the same language, no matter who makes the device.
When you move the slider it doesn't send over the network "set the bulb to this color that's kinda warmish but not too warm" it says "set bulb to 4000K." Although homekit uses
Mired instead of degrees kelvin, but mired is just "1,000,000/kelvin" so it's easy to figure out. 4,000k = 250 mired
The number exists in the app, they just don't display it
in the same way that people have standardized the temperature scale, They have done the same for color temperature and color. They might use different scales like Celsius/Fahrenheit or Kelvin/Mired, but it's typically simple math to convert between. All 3 have nothing to do with apple and have existed LONG before homekit (or apple) was even a thing.
When you say "give me a pot of water at 120F," you will always get you the same result. Although some might give you water at 49C. And some might be poor with their accuracy so your water might be between 115-125F, but it'll be close.
you can apply the same to color and color temperature, some might use hue+saturation some might use X,Y and some cheaper devices might not match exactly, but they'll all come out the same color or at least close.
the devices also talk back to the home app, so it knows what range it can set bulbs to.
If you had a white and a white+color bulb from hue, and look at their individual color temperature setting screen, they probably look slightly different. I have a variable white LED strip that does 2400-6500, and it's slightly different from the hue bulb's.
the fixed white bulb, homekit doesn't even know or care what color temperature it is, only that it can turn on/off and dim.
if you were to ask siri to set a light to 2,100K
the fixed white bulb would do nothing, since it has no color paramters
the white ambiance would do nothing, since it's outside it's supported range
the white/color would change, since it's supported
but if you said "set the light to 3,000K"
again the fixed white would do nothing
the white and white/color would both change.