cannot update apps installed with machine scope using winget in the system context

Brief description of your issue

I installed ungoogled chromium using the following command:

winget install -e --id eloston.ungoogled-chromium --interactive --scope machine --architecture x64

or NAPS2 with:

winget install -e --id Cyanfish.NAPS2 --interactive --scope machine --architecture x64

Now, when I try to update using winget running in the system context, it doesn't recognize these applications, and as a result, it doesn't update them.

Now I don't know how to trace this back if it's an issue with the installation file, to understand what the problem might be.

Using this program (https://github.com/Romanitho/Winget-AutoUpdate), I've come to the point where winget doesn't recognize these software applications in the system context (in this issue are the details https://github.com/Romanitho/Winget-AutoUpdate/issues/362). However, it's also possible that winget doesn't recognize them because something goes wrong during the installation.

Steps to reproduce

1. Install ungoogled chromium using the following command:

   winget install -e --id eloston.ungoogled-chromium --interactive --scope machine --architecture x64
   

2. Alternatively, install NAPS2 with:

   winget install -e --id Cyanfish.NAPS2 --interactive --scope machine --architecture x64
   

3. When attempting to update using winget in the system context, it fails to recognize these applications (tested with winget export), resulting in an inability to update them.

Expected behavior

The ability to update these applications in the system context.

Actual behavior

It cannot be updated with winget when using it in the system context.

Environment

Windows Package Manager v1.6.3133
Copyright (c) Microsoft Corporation. All rights reserved.

Windows: Windows.Desktop v10.0.22631.2715
System Architecture: X64
Package: Microsoft.DesktopAppInstaller v1.21.3133.0

Winget Directories
-------------------------------------------------------------------------------------------------------------------------------
Logs                               %LOCALAPPDATA%\Packages\Microsoft.DesktopAppInstaller_8wekyb3d8bbwe\LocalState\DiagOutputDir
User Settings                      %LOCALAPPDATA%\Packages\Microsoft.DesktopAppInstaller_8wekyb3d8bbwe\LocalState\settings.json
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

Reproduce the issue with the ungoogled-chromium or NAPS2 commands, then compare winget export results when run normally and in the system context. Use the supplied environment details and logs directory to trace why machine-scope installations are not recognized; done means the applications can be detected and updated in the system context.