Then that means there is a possibility manifest problem. Either way, you should be seeing the Add to Homescreen in the chrome menu. If it’s a PWA, it will install the app. If it’s not a PWA, it will only add a bookmark to the Homescreen. Are you saying that it’s adding a bookmark with the chrome logo? Or do you not see the add to Homescreen option at all?
Again, please confirm the browser you are using.
Since there is no button to install the app, you could include instructions to install the app in place of a button.
Here’s one you could use: