Login from computer and install app on device from website
I don't see any other proposal of this kind...
It would be useful to be able to register and login from the website (and from the f-droid app with same credentials) in order to install apps directly from website.
Now if users find an app browsing the website from their computer, they must open the f-droid app on the phone, search again the app, and click the button to install it.
It would be much quicker if the browser on the computer and the f-droid app on the phone(s) are connected, like Google Play, and with a simple button the user can choose on which phone(s) install the selected app.