Add telemetry for shortcut conflict detection feature. (#41271)

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## Summary of the Pull Request
Add telemetry for shortcut conflict detection.

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## PR Checklist

- [ ] Closes: #xxx
- [ ] **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
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- [ ] [WXS for
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pipeline](https://github.com/microsoft/PowerToys/blob/main/.pipelines/ci/templates/build-powertoys-steps.yml)
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- [ ] **Documentation updated:** If checked, please file a pull request
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and link it here: #xxx

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---------

Signed-off-by: Shawn Yuan <shuaiyuan@microsoft.com>
Signed-off-by: Shuai Yuan <shuai.yuan.zju@gmail.com>

src/settings-ui/Settings.UI/SettingsXAML/Controls/Dashboard/ShortcutConflictControl.xaml.cs

@@ -7,7 +7,9 @@ using System.Collections.Generic;
 using System.ComponentModel;
 using System.Linq;
 using Microsoft.PowerToys.Settings.UI.Library.HotkeyConflicts;
+using Microsoft.PowerToys.Settings.UI.Library.Telemetry.Events;
 using Microsoft.PowerToys.Settings.UI.SettingsXAML.Controls.Dashboard;
+using Microsoft.PowerToys.Telemetry;
 using Microsoft.UI.Xaml;
 using Microsoft.UI.Xaml.Controls;
 using Microsoft.Windows.ApplicationModel.Resources;
@@ -18,6 +20,8 @@ namespace Microsoft.PowerToys.Settings.UI.Controls
     {
         private static readonly ResourceLoader ResourceLoader = Helpers.ResourceLoaderInstance.ResourceLoader;
 
+        private static bool _telemetryEventSent;
+
         public static readonly DependencyProperty AllHotkeyConflictsDataProperty =
             DependencyProperty.Register(
                 nameof(AllHotkeyConflictsData),
@@ -92,6 +96,17 @@ namespace Microsoft.PowerToys.Settings.UI.Controls
 
             // Update visibility based on conflict count
             Visibility = HasConflicts ? Visibility.Visible : Visibility.Collapsed;
+
+            if (!_telemetryEventSent && HasConflicts)
+            {
+                // Log telemetry event when conflicts are detected
+                PowerToysTelemetry.Log.WriteEvent(new ShortcutConflictDetectedEvent()
+                {
+                    ConflictCount = ConflictCount,
+                });
+
+                _telemetryEventSent = true;
+            }
         }
 
         private void OnPropertyChanged(string propertyName)
@@ -115,6 +130,12 @@ namespace Microsoft.PowerToys.Settings.UI.Controls
                 return;
             }
 
+            // Log telemetry event when user clicks the shortcut conflict button
+            PowerToysTelemetry.Log.WriteEvent(new ShortcutConflictControlClickedEvent()
+            {
+                ConflictCount = this.ConflictCount,
+            });
+
             // Create and show the new window instead of dialog
             var conflictWindow = new ShortcutConflictWindow();