check if user has already installed PWA to homescreen on Chrome?

Perhaps, don’t show the button until you intercept the automatic pop-up?

or
In your code, check to see if the window is standalone
If it is, you need not show the button

if (window.matchMedia('(display-mode: standalone)').matches) {  
    // do things here  
    // set a variable to be used when calling something  
    // e.g. call Google Analytics to track standalone use   
}  

My example tester here
https://a2hs.glitch.me

Source code for my tester
https://github.com/ng-chicago/AddToHomeScreen