CmdPal: Window Walker - reevaluate process type when window process is updated (#42317)

## Summary of the Pull Request

This PR moves `ProcessPackagingInspector.Inspect` from the
`WindowProcess` constructor to `UpdateProcessInfo`, ensuring the process
type is correctly re-evaluated when the window’s backing process changes
(as with UWP apps hosted in `ApplicationFrameHost.exe`).

See
4d47659ff9/src/modules/cmdpal/ext/Microsoft.CmdPal.Ext.WindowWalker/Components/Window.cs (L295-L350)

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## PR Checklist

- [x] Closes: #38353 
- [ ] **Communication:** I've discussed this with core contributors
already. If the work hasn't been agreed, this work might be rejected
- [ ] **Tests:** Added/updated and all pass
- [ ] **Localization:** All end-user-facing strings can be localized
- [ ] **Dev docs:** Added/updated
- [ ] **New binaries:** Added on the required places
- [ ] [JSON for
signing](https://github.com/microsoft/PowerToys/blob/main/.pipelines/ESRPSigning_core.json)
for new binaries
- [ ] [WXS for
installer](https://github.com/microsoft/PowerToys/blob/main/installer/PowerToysSetup/Product.wxs)
for new binaries and localization folder
- [ ] [YML for CI
pipeline](https://github.com/microsoft/PowerToys/blob/main/.pipelines/ci/templates/build-powertoys-steps.yml)
for new test projects
- [ ] [YML for signed
pipeline](https://github.com/microsoft/PowerToys/blob/main/.pipelines/release.yml)
- [ ] **Documentation updated:** If checked, please file a pull request
on [our docs
repo](https://github.com/MicrosoftDocs/windows-uwp/tree/docs/hub/powertoys)
and link it here: #xxx

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## Detailed Description of the Pull Request / Additional comments

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## Validation Steps Performed

src/modules/cmdpal/ext/Microsoft.CmdPal.Ext.WindowWalker/Components/Window.cs

@@ -324,7 +324,7 @@ internal sealed class Window
 
             // Correct the process data if the window belongs to a uwp app hosted by 'ApplicationFrameHost.exe'
             // (This only works if the window isn't minimized. For minimized windows the required child window isn't assigned.)
-            if (string.Equals(_handlesToProcessCache[hWindow].Name, "ApplicationFrameHost.exe", StringComparison.OrdinalIgnoreCase))
+            if (_handlesToProcessCache[hWindow].IsUwpAppFrameHost)
             {
                 new Task(() =>
                 {

src/modules/cmdpal/ext/Microsoft.CmdPal.Ext.WindowWalker/Components/WindowProcess.cs

@@ -23,7 +23,7 @@ internal sealed class WindowProcess
     /// <summary>
     /// An indicator if the window belongs to an 'Universal Windows Platform (UWP)' process
     /// </summary>
-    private readonly bool _isUwpAppFrameHost;
+    private bool _isUwpAppFrameHost;
 
     /// <summary>
     /// Gets the id of the process
@@ -126,6 +126,14 @@ internal sealed class WindowProcess
         get; private set;
     }
 
+    /// <summary>
+    /// Gets the type of the process (UWP app, packaged Win32 app, unpackaged Win32 app, ...).
+    /// </summary>
+    internal ProcessPackagingInfo ProcessType
+    {
+        get; private set;
+    }
+
     /// <summary>
     /// Initializes a new instance of the <see cref="WindowProcess"/> class.
     /// </summary>
@@ -134,13 +142,10 @@ internal sealed class WindowProcess
     /// <param name="name">New process name.</param>
     internal WindowProcess(uint pid, uint tid, string name)
     {
+        ProcessType = ProcessPackagingInfo.Empty;
         UpdateProcessInfo(pid, tid, name);
-        ProcessType = ProcessPackagingInspector.Inspect((int)pid);
-        _isUwpAppFrameHost = string.Equals(Name, "ApplicationFrameHost.exe", StringComparison.OrdinalIgnoreCase);
     }
 
-    public ProcessPackagingInfo ProcessType { get; private set; }
-
     /// <summary>
     /// Updates the process information of the <see cref="WindowProcess"/> instance.
     /// </summary>
@@ -156,6 +161,10 @@ internal sealed class WindowProcess
 
         // Process can be elevated only if process id is not 0 (Dummy value on error)
         IsFullAccessDenied = (pid != 0) ? TestProcessAccessUsingAllAccessFlag(pid) : false;
+
+        // Update process type
+        ProcessType = ProcessPackagingInspector.Inspect((int)pid);
+        _isUwpAppFrameHost = string.Equals(Name, "ApplicationFrameHost.exe", StringComparison.OrdinalIgnoreCase);
     }
 
     /// <summary>

src/modules/cmdpal/ext/Microsoft.CmdPal.Ext.WindowWalker/Helpers/ProcessPackagingInfo.cs

@@ -11,4 +11,13 @@ internal sealed record ProcessPackagingInfo(
     bool IsAppContainer,
     string? PackageFullName,
     int? LastError
-);
+)
+{
+    public static ProcessPackagingInfo Empty { get; } = new(
+        Pid: 0,
+        Kind: ProcessPackagingKind.Unknown,
+        HasPackageIdentity: false,
+        IsAppContainer: false,
+        PackageFullName: null,
+        LastError: null);
+}