.NET 5 changes some behaviour of single-file applications. By default, native libraries aren't bundled and therefore must be copied over along with the executable during deployment. Currently, only the executable is deployed so deployment is basically broken. The fix is to set IncludeNativeLibrariesForSelfExtract to bundle the native libraries. It's unclear if this will work on the deployment server but I think most of the previous issues were more related to app trimming. If it is unsuccessful, the deployment could of course just copy over the DLLs too.
See https://docs.microsoft.com/en-us/dotnet/core/deploying/single-file#other-considerations for reference.