You can browse the App Store on your Mac/Windows PC and install apps on your iOS devices by installing iTunes 12.6.3 with App Store support. More information and download links are available in the Apple Support article, Deploy apps in a business environment with iTunes.
As far as the options shown in the screenshot are concerned, it enables automatic installation of apps purchased on other devices which are logged into with the same Apple ID as this device.
To further clarify, using the mentioned setting enabled, your iPhone will only download any new apps purchased either on any other iOS device linked with the same Apple ID or Mac/PC with iTunes 12.6.3 or older installed and logged in with the same Apple ID. It can't be used to install any previously purchased app not already installed on your iPhone.
Installing iTunes 12.6.3 is the only resort for the time being if you wish to manually sync apps from your iTunes library.