[Package Issue]: Microsoft.DotNet.SDK.9

Nobody has claimed this yet.

### Please confirm these before moving forward

- [x] I have searched for my issue and not found a work-in-progress/duplicate/resolved issue.
- [x] I have not been informed if the issue is resolved in a preview version of the winget client.

### Category of the issue

Other

### Brief description of your issue

the package lacks a "scope", showing as "Unknown", while clearly being installed in a "machine" context

### Steps to reproduce

winget install --verbose Microsoft.DotNet.SDK.9 --architecture=x86 --scope=machine
winget install --verbose Microsoft.DotNet.SDK.9 --architecture=x64 --scope=machine

### Actual behavior

the package cannot be installed when a scope is demanded by external environment

### Expected behavior

the package should have "scope" defined as "machine"

### Environment

```raw
Windows-Paket-Manager v1.12.350
Copyright (c) Microsoft Corporation. Alle Rechte vorbehalten.

Windows: Windows.Desktop v10.0.26200.7019
Systemarchitektur: X64
Paket: Microsoft.DesktopAppInstaller v1.27.350.0

WinGet-Verzeichnisse
-----------------------------------------------------------------------------------------------------------------------
Protokolle %LOCALAPPDATA%\Packages\Microsoft.DesktopAppInstaller_8wekyb3d8bbwe\Local…
Benutzereinstellungen %LOCALAPPDATA%\Packages\Microsoft.DesktopAppInstaller_8wekyb3d8bbwe\Local…
Verzeichnis für portierbare Links (Benutzer) %LOCALAPPDATA%\Microsoft\WinGet\Links
Portables Linkverzeichnis (Computer) C:\Program Files\WinGet\Links
Portierbarer Paketstamm (Benutzer) %LOCALAPPDATA%\Microsoft\WinGet\Packages
Portierbarer Paketstamm C:\Program Files\WinGet\Packages
Portierbares Paketstamm (x86) C:\Program Files (x86)\WinGet\Packages
Installationsprogrammdownloads %USERPROFILE%\Downloads
Konfigurationsmodule %LOCALAPPDATA%\Microsoft\WinGet\Configuration\Modules

Links
-----------------------------------------------------------------------------------------
Datenschutzerklärung https://aka.ms/winget-privacy
Lizenzvereinbarung https://aka.ms/winget-license
Hinweise von Drittanbietern https://aka.ms/winget-3rdPartyNotice
Startseite https://aka.ms/winget
Windows Store-Nutzungsbedingungen https://www.microsoft.com/en-us/storedocs/terms-of-sale

Administratoreinstellung Status
-----------------------------------------------------
LocalManifestFiles Deaktiviert
BypassCertificatePinningForMicrosoftStore Deaktiviert
InstallerHashOverride Deaktiviert
LocalArchiveMalwareScanOverride Deaktiviert
ProxyCommandLineOptions Deaktiviert
DefaultProxy Deaktiviert
```

### Screenshots and Logs

_No response_

Search the repository for the Microsoft.DotNet.SDK.9 package entry and inspect how its installer scope is represented. Reproduce the issue with the two provided winget install commands using --scope=machine, then verify that the package reports machine scope and installs successfully when scope is required.

Written by the indexing model from the issue text.