Okay, I finally solved it: this seems to be related to the TargetFramework I had defined in my .csproj:

This version doesn't allow drag/drop in my MSIX app (I have the same issue in a completely new WPF project):

<TargetFramework>net6.0-windows10.0.22621.0</TargetFramework>

This version works without issues:

<TargetFramework>net6.0-windows10.0.19041.0</TargetFramework>

The former being a Windows 11 .net, which I guess somehow doesn't allow drag/drop for some reason (at least for me.)