The EmailManager API is only supported with UWP apps, because it depends on Windows.UI.Core.CoreWindow Class's GetForCurrentThread method which always get backs null for non-UWP apps.

You can check this dependency if you disassemble the ShowComposeNewEmailAsync function, as shown in this screenshot here:

Some of these WinRT classes have been modified to support the IInitializeWindow trick to support classical HWNDs, but it seems it's not the case here. Maybe you can report that to Microsoft so they can improve it.

So you'll have to find other non-WinRT/UWP ways to send email.