It is possible... It's fidgety, but possible.
You need to add an OUT to the same button with LED as the type of controller and Interaction mode to output.
Set the controller range Min=0 & Max=1. Midi range stays at Min=0 and Max=127.
Tricky bit number 1 - Make sure you are not using latching layers and to choose your button color (red, green or orange) you need to consult the manual for the corresponding midi note (CC or note detc etc), then manually enter that value into the button value field e.g Ch15.Note.C#1 or what ever the corresponding one is for your button.
Tricky bit number 2 - It doesnt always light up when you start up or connect your K2.. you need to press the button for it to start working sometimes.
Here is the manual. Page 17+18 for the MIDI Out designations:
Disable latching layers is a first thing you need to do in order to access all 3 colors in the same layout.
If you share some screenshots of your hotcue commands then you would get a better answer.
Post some screenshots, we don't know what command are you using to output cues.
Check official A&H youtube channel, you will find info on how to disable layer system.
The manual i linked describes how to activate and deactivate latching layers.
You are using incorrect output command.
Add Out --> Track Deck --> Cue --> Hotcue X Type (there is dedicated command for each cue)
https://www.youtube.com/watch?v=96Kmd8BPiWM&ab_channel=AllenandHeathUK
It is "State 1" of the Latching Layers setup^