In 2022 and earlier there were two ways to make the screen color eye dropper work. In 2023 only one of those two ways works. In the internal version I have, only the other way works!
The two ways of working were to either click the icon, then click anywhere on the screen. Most likely that would send SketchUp into the background, but at least the color had changed.
The other way was to click anywhere in the SketchUp windows, then drag, and release when you are over the color in another application. That had the benefit that you remained in SketchUp.
In the version you have, choose the eyedropper, click inside any SketchUp window, then drag, and release when you are over the color you want to grab.
In the version I have, I immediately click on the color anywhere on the screen, but, I am most likely going to switch to that other application.
The way 2022 had it was nice, that you had the option. From now on it looks like you will only have one way of doing it.