That's probably beyond the scope of this forum. You'd need to use some JS to set the value.
One thing you can do that is Keyboard Maestro related, is to use KM in your JS code to format the date. You can call Keyboard Maestro's "Process Tokens", and combine it with "%ICUDateTimeFor%".
See the following:
https://wiki.keyboardmaestro.com/action/Custom_HTML_Prompt, specifically "window.KeyboardMaestro.ProcessTokens()".
https://wiki.keyboardmaestro.com/token/ICUDateTime, specifically the reference to "%ICUDateTimeFor% TIME(2015, 8, 23,12,0,0) %EEE, MMM d, yyyy%"
I realize that's not a detailed answer, and the examples shown will require some trial and error to get them working for your situation, but at least it's something.