fixed light switch shortcut not working issue (#42340)

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fix/what does it change/how was it tested (even manually, if necessary)?
-->
## Summary of the Pull Request
This pull request refactors how the `ToggleThemeHotkey` property is
handled in the LightSwitch settings and view model. The changes simplify
property management by directly referencing the property within
`LightSwitchProperties` and ensure that the hotkey setting is
consistently updated and serialized.

**Settings property management:**

* In `LightSwitchSettings.Clone()`, the `LightSwitchProperties` object
now directly references the existing property instances instead of
creating new ones, and also includes the `ToggleThemeHotkey` property.

**View model property handling:**

* In `LightSwitchViewModel.ToggleThemeActivationShortcut`, the getter
and setter now directly access and update
`ModuleSettings.Properties.ToggleThemeHotkey.Value`, removing the need
for a backing field and ensuring changes are properly serialized and
notified.
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## PR Checklist

- [x] Closes: #42330
- [ ] **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

<!-- Provide a more detailed description of the PR, other things fixed,
or any additional comments/features here -->
## Detailed Description of the Pull Request / Additional comments

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wherever possible, but list manual validation steps taken as well -->
## Validation Steps Performed

---------

Signed-off-by: Shawn Yuan (from Dev Box) <shuaiyuan@microsoft.com>

src/settings-ui/Settings.UI/ViewModels/LightSwitchViewModel.cs

@@ -3,6 +3,7 @@
 // See the LICENSE file in the project root for more information.
 
 using System;
+using System.Collections.Generic;
 using System.Collections.ObjectModel;
 using System.Globalization;
 using System.Linq;
@@ -20,8 +21,10 @@ using Settings.UI.Library.Helpers;
 
 namespace Microsoft.PowerToys.Settings.UI.ViewModels
 {
-    public partial class LightSwitchViewModel : Observable
+    public partial class LightSwitchViewModel : PageViewModelBase
     {
+        protected override string ModuleName => LightSwitchSettings.ModuleName;
+
         private Func<string, int> SendConfigMSG { get; }
 
         public ObservableCollection<SearchLocation> SearchLocations { get; } = new();
@@ -35,14 +38,24 @@ namespace Microsoft.PowerToys.Settings.UI.ViewModels
             ForceDarkCommand = new RelayCommand(ForceDarkNow);
 
             AvailableScheduleModes = new ObservableCollection<string>
-        {
-            "FixedHours",
-            "SunsetToSunrise",
-        };
+            {
+                "FixedHours",
+                "SunsetToSunrise",
+            };
 
             _toggleThemeHotkey = _moduleSettings.Properties.ToggleThemeHotkey.Value;
         }
 
+        public override Dictionary<string, HotkeySettings[]> GetAllHotkeySettings()
+        {
+            var hotkeysDict = new Dictionary<string, HotkeySettings[]>
+            {
+                [ModuleName] = [ToggleThemeActivationShortcut],
+            };
+
+            return hotkeysDict;
+        }
+
         private void ForceLightNow()
         {
             Logger.LogInfo("Sending custom action: forceLight");
@@ -395,22 +408,21 @@ namespace Microsoft.PowerToys.Settings.UI.ViewModels
 
         public HotkeySettings ToggleThemeActivationShortcut
         {
-            get => _toggleThemeHotkey;
+            get => ModuleSettings.Properties.ToggleThemeHotkey.Value;
 
             set
             {
-                if (value != _toggleThemeHotkey)
+                if (value != ModuleSettings.Properties.ToggleThemeHotkey.Value)
                 {
                     if (value == null)
                     {
-                        _toggleThemeHotkey = LightSwitchProperties.DefaultToggleThemeHotkey;
+                        ModuleSettings.Properties.ToggleThemeHotkey.Value = LightSwitchProperties.DefaultToggleThemeHotkey;
                     }
                     else
                     {
-                        _toggleThemeHotkey = value;
+                        ModuleSettings.Properties.ToggleThemeHotkey.Value = value;
                     }
 
-                    _moduleSettings.Properties.ToggleThemeHotkey.Value = _toggleThemeHotkey;
                     NotifyPropertyChanged();
 
                     SendConfigMSG(
@@ -418,7 +430,7 @@ namespace Microsoft.PowerToys.Settings.UI.ViewModels
                             CultureInfo.InvariantCulture,
                             "{{ \"powertoys\": {{ \"{0}\": {1} }} }}",
                             LightSwitchSettings.ModuleName,
-                            JsonSerializer.Serialize(_moduleSettings, (System.Text.Json.Serialization.Metadata.JsonTypeInfo<LightSwitchSettings>)SourceGenerationContextContext.Default.LightSwitchSettings)));
+                            JsonSerializer.Serialize(_moduleSettings, SourceGenerationContextContext.Default.LightSwitchSettings)));
                 }
             }
         }