CmdPal: Add option to return to home automatically after a delay (#43551)

## Summary of the Pull Request

This PR replaces the Go home when activated setting with a new
Automatically return home option. This allows users to specify how long
the Command Palette should wait after being dismissed before
automatically returning to the home page. It also introduces migration
logic to transition from the old setting to the new one.

## Pictures? Pictures!

<img width="1337" height="762" alt="image"
src="https://github.com/user-attachments/assets/c649ef03-b3ee-40ba-ac67-485bc40efa73"
/>


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## PR Checklist

- [x] Closes: #43355 
<!-- - [ ] Closes: #yyy (add separate lines for additional resolved
issues) -->
- [ ] **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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or any additional comments/features here -->
## Detailed Description of the Pull Request / Additional comments

<!-- Describe how you validated the behavior. Add automated tests
wherever possible, but list manual validation steps taken as well -->
## Validation Steps Performed

src/modules/cmdpal/Microsoft.CmdPal.UI.ViewModels/SettingsViewModel.cs

@@ -11,6 +11,19 @@ namespace Microsoft.CmdPal.UI.ViewModels;
 
 public partial class SettingsViewModel : INotifyPropertyChanged
 {
+    private static readonly List<TimeSpan> AutoGoHomeIntervals =
+    [
+        Timeout.InfiniteTimeSpan,
+        TimeSpan.Zero,
+        TimeSpan.FromSeconds(10),
+        TimeSpan.FromSeconds(20),
+        TimeSpan.FromSeconds(30),
+        TimeSpan.FromSeconds(60),
+        TimeSpan.FromSeconds(90),
+        TimeSpan.FromSeconds(120),
+        TimeSpan.FromSeconds(180),
+    ];
+
     private readonly SettingsModel _settings;
     private readonly IServiceProvider _serviceProvider;
 
@@ -58,16 +71,6 @@ public partial class SettingsViewModel : INotifyPropertyChanged
         }
     }
 
-    public bool HotkeyGoesHome
-    {
-        get => _settings.HotkeyGoesHome;
-        set
-        {
-            _settings.HotkeyGoesHome = value;
-            Save();
-        }
-    }
-
     public bool BackspaceGoesBack
     {
         get => _settings.BackspaceGoesBack;
@@ -138,6 +141,25 @@ public partial class SettingsViewModel : INotifyPropertyChanged
         }
     }
 
+    public int AutoGoBackIntervalIndex
+    {
+        get
+        {
+            var index = AutoGoHomeIntervals.IndexOf(_settings.AutoGoHomeInterval);
+            return index >= 0 ? index : 0;
+        }
+
+        set
+        {
+            if (value >= 0 && value < AutoGoHomeIntervals.Count)
+            {
+                _settings.AutoGoHomeInterval = AutoGoHomeIntervals[value];
+            }
+
+            Save();
+        }
+    }
+
     public ObservableCollection<ProviderSettingsViewModel> CommandProviders { get; } = [];
 
     public SettingsExtensionsViewModel Extensions { get; }