How to restore message green icon on iPhone 12 Pro Max? In apple store shows to open the app but no option to download

"Open" indicates that it is currently installed on your iPhone. Go to the App Library (swipe left past your last home screen). From there you can touch and hold an app and slide it left back to the home screen.

There is a Search box at the top of the App Library screen if needed.

Apps can be removed from the Home Screen without being deleted.