I am creating a windows 10 universal app targeted for both Windows Phones and Windows Desktop, the problem I am facing on is when adding splash screen through the package.manifest file to the app, there is no option to add splash screen which fits the phone's portrait orientation (see the image below),
And when I deploy the app on the phone the splash screen appears like shown below.
In this case, you will also want to specify the Background color, on your first screenshot.
Read this -
For a Windows Phone Store app, provide the 2.4x asset at a minimum; preferably all. The image file assets themselves should have a transparent background. In your app manifest, set the value of the SplashScreen@Image property to "Assets\.png", and set a value for VisualElements@BackgroundColor.
You can read more from this link.
The first half of the link seems to be talking about splash screens in the Windows 8.1 & Windows Phone 8.1, including the paragraph I quoted above, but the same rules apply to Windows 10. I don't think you can have a full page splash screen given all the different sized devices. Previously it would still be possible 'cause you could simply remove the splash screen and create a xaml startup usercontrol within your app, but since the splash screen becomes mandatory in UWP, I just don't see any other way to achieve this.