Enhance the winget install check

scripts/Windows/OS/Install.ps1

@@ -65,7 +65,7 @@ $null = New-Module {
                     Install-Module -AcceptLicense -Force PSWindowsUpdate;
                 };
 
-                if (-not (Test-Command winget)) {
+                if (-not (Test-Winget)) {
                     . "$PSScriptRoot/../Software/winget/Manage.ps1";
                     continue;
                 }

scripts/Windows/Scripts/SoftwareManagement.ps1

@@ -57,6 +57,17 @@ function Test-Command {
     [bool] (Get-Command $Name -ErrorAction SilentlyContinue);
 }
 
+<#
+    .SYNOPSIS
+    Checks whether `winget` is working properly.
+#>
+function Test-Winget {
+    (Test-Command winget) -and -not (
+        [System.Linq.Enumerable]::Any(
+            [string[]](winget source update winget),
+            [System.Func[string,bool]]{ param($line) $line -eq "Cancelled"; }));
+}
+
 <#
     .SYNOPSIS
     Checks whether a package with the specified name is installed.