It's probably just a normal button that is hardcoded to run a specific AI software that is installed on your system (as it is indicated by "Launches AI Prompt Builder"). Just a guess. There is no need for a dedicated button, as any extra button could be configured to do the same.
Only people with an artificial brain will fall for this.
You can already use with with any Logitech mouse in the Options+ Software.
It is what it says: it builds a prompt for you (with the text you marked) and can submit it to ChatGPT using a WebView. You have to actually login to ChatGPT, so it is no Logitech thing specifically.
It's inevitable. Your competitors are using ai. You have to implement it to not get behind. No one cares beyond being able to slap a label on the product.
You might like to think that from your point of view, but the executives and marketing folks get that idea from somewhere. And if it would not make additional money it would have been gone again already.