WinRT.Runtime conflict in PowerShell 7.3.8

Brief description of your issue

I am running version 0.2.2 of the Microsoft.Winget.Client module, although I had this problem in the earlier version. In a PowerShell 7 session running with no profile, I can import and use the module with no problem. In my normal session, with a profile, I can import the module with no errors. But when I run any command, I get the error The type initializer for '<Module>' threw an exception.

I've narrowed down at least part of the problem to the fact that not all DLLs are getting loaded. I think the WinRT.Runtime is the culprit. I tried manually adding it in my PowerShell session and it fails.

PSMessageDetails      :
Exception             : System.IO.FileLoadException: Could not load file or assembly 'WinRT.Runtime, Version=2.0.0.0,
                        Culture=neutral, PublicKeyToken=99ea127f02d97709'.
                           at System.Runtime.Loader.AssemblyLoadContext.<LoadFromPath>g____PInvoke|5_0(IntPtr
                        ptrNativeAssemblyBinder, UInt16* ilPath, UInt16* niPath, ObjectHandleOnStack retAssembly)
                           at System.Runtime.Loader.AssemblyLoadContext.LoadFromAssemblyPath(String assemblyPath)
                           at System.Reflection.Assembly.LoadFrom(String assemblyFile)
                           at Microsoft.PowerShell.Commands.AddTypeCommand.LoadAssemblies(IEnumerable`1 assemblies)
                           at System.Management.Automation.CommandProcessorBase.Complete()
TargetObject          :
CategoryInfo          : NotSpecified: (:) [Add-Type], FileLoadException
FullyQualifiedErrorId : System.IO.FileLoadException,Microsoft.PowerShell.Commands.AddTypeCommand
ErrorDetails          :
InvocationInfo        : System.Management.Automation.InvocationInfo
ScriptStackTrace      : at <ScriptBlock>, <No file>: line 1
PipelineIterationInfo : {}
```a 

### Steps to reproduce

I can't give you steps to reproduce.  I'm hoping for guidance on how to figure out what might be conflicting with the WinRT.Runtime assembly.

### Expected behavior

Commands should work as expected.

### Actual behavior

```powershell
PS C:\> get-wingetsettings -Verbose
Get-WinGetSettings: The type initializer for '<Module>' threw an exception.

Environment

Windows Package Manager v1.6.2771
Copyright (c) Microsoft Corporation. All rights reserved.

Windows: Windows.Desktop v10.0.22624.1391
System Architecture: X64
Package: Microsoft.DesktopAppInstaller v1.21.2771.0

Winget Directories                 
-----------------------------------------------------------------------------------------------------------------------
Logs                               %LOCALAPPDATA%\Packages\Microsoft.DesktopAppInstaller_8wekyb3d8bbwe\LocalState\Diag…
User Settings                      %LOCALAPPDATA%\Packages\Microsoft.DesktopAppInstaller_8wekyb3d8bbwe\LocalState\sett…
Portable Links Directory (User)    %LOCALAPPDATA%\Microsoft\WinGet\Links
Portable Links Directory (Machine) C:\Program Files\WinGet\Links
Portable Package Root (User)       %LOCALAPPDATA%\Microsoft\WinGet\Packages
Portable Package Root              C:\Program Files\WinGet\Packages
Portable Package Root (x86)        C:\Program Files (x86)\WinGet\Packages
Installer Downloads                %USERPROFILE%\Downloads

Links               
---------------------------------------------------------------------------
Privacy Statement   https://aka.ms/winget-privacy
License Agreement   https://aka.ms/winget-license
Third Party Notices https://aka.ms/winget-3rdPartyNotice
Homepage            https://aka.ms/winget
Windows Store Terms https://www.microsoft.com/en-us/storedocs/terms-of-sale

Admin Setting                             State
--------------------------------------------------
LocalManifestFiles                        Disabled
BypassCertificatePinningForMicrosoftStore Disabled
InstallerHashOverride                     Disabled
LocalArchiveMalwareScanOverride           Disabled

Name                           Value
----                           -----
PSVersion                      7.3.8
PSEdition                      Core
GitCommitId                    7.3.8
OS                             Microsoft Windows 10.0.22624
Platform                       Win32NT
PSCompatibleVersions           {1.0, 2.0, 3.0, 4.0…}
PSRemotingProtocolVersion      2.3
SerializationVersion           1.1.0.1
WSManStackVersion              3.0

Start with the Microsoft.Winget.Client module in a normal PowerShell 7.3.8 session, comparing it with a no-profile session. Reproduce the failure through Get-WinGetSettings and inspect the Add-Type attempt to load WinRT.Runtime. Done means identifying the conflicting assembly or loading condition and making the module commands work in the reported environment.