I attempted installs of Xperience 13 Refresh9 and also Refresh11 with the same results documented below. Please note that these same steps work on a Kentico 12 installation.
I am following instructions from a combination of the below:
https://docs.kentico.com/13/integrating-3rd-party-systems/using-asp-net-web-api-with-xperience
https://stackoverflow.com/questions/47581678/trying-to-use-kentico-with-powershell
Specificall,y trying to Import-Module the assemblies CMS.DataEngine.dll and CMS.Membership.dll in the current session to execute [CMS.DataEngine.CMSApplication]::Init() and [CMS.Membership.UserInfoProvider]::GetUserInfo($CMSUser).
Although I see that the project has a dependency to Microsoft.Extensions.DependencyInjection.Abstractions v3.1.8.0, attempts to load CMS.DataEngine.dll all fail with below error:
Exception calling "Init" with "0" argument(s): "Could not load file or assembly 'Microsoft.Extensions.DependencyInjection.Abstractions, Version=3.1.0.0, Culture=neutral,
PublicKeyToken=adb9793829ddae60' or one of its dependencies. The system cannot find the file specified."
+ CategoryInfo : NotSpecified: (:) [Write-Error], WriteErrorException
+ FullyQualifiedErrorId : Microsoft.PowerShell.Commands.WriteErrorException
The project has in Lib\, CMS\bin and in the Kentico v13 Program itself under bin\CMS directories only assemblies of version 3.1.8.0 for this package. Attempts to downgrade the packages end up with circular dependencies in downgrades to other Microsoft.* packages and break Xperience 13 completely.
Edit: I am seeing the same error with both MVC5 and Core Kentico v13.