The issue to get Winget recognized behind system context will be solved with this command:
Add-AppxPackage -RegisterByFamilyName -MainPackage Microsoft.DesktopAppInstaller_8wekyb3d8bbwe
But the major issue in Winget is, that it does not use winget resource after OS installation or windows enrollment, it will then use only msstore repository. I have MS case opened because of this. I will keep your posted.