[Feature] PowerToys hotkey conflict detection (#41029)

<!-- Enter a brief description/summary of your PR here. What does it
fix/what does it change/how was it tested (even manually, if necessary)?
-->
## Summary of the Pull Request
Implements comprehensive hotkey conflict detection and resolution system
for PowerToys, providing real-time conflict checking and centralized
management interface.

## PR Checklist

- [ ] **Closes:** #xxx
- [x] **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
- [x] **Localization:** All end-user-facing strings can be localized
- [x] **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)
- [x] **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: [Shortcut conflict detction dev
spec](https://github.com/MicrosoftDocs/windows-dev-docs/pull/5519)

## TODO Lists
- [x] Add real-time hotkey validation functionality to the hotkey dialog
- [x] Immediately detect conflicts and update shortcut conflict status
after applying new shortcuts
- [x] Return conflict list from runner hotkey conflict detector for
conflict checking.
- [x] Implement the Tooltip for every shortcut control 
- [x] Add dialog UI for showing all the shortcut conflicts
- [x] Support changing shortcut directly inside the shortcut conflict
window/dialog, no need to nav to the settings page.
- [x] Redesign the `ShortcutConflictDialogContentControl` to align with
the spec
- [x] Add navigating and changing hotkey auctionability to the
`ShortcutConflictDialogContentControl`
- [x] Add telemetry. Impemented in [another
PR](https://github.com/shuaiyuanxx/PowerToys/pull/47)

## Shortcut Conflict Support Modules

![image](https://github.com/user-attachments/assets/3915174e-d1e7-4f86-8835-2a1bafcc85c9)

<details>
<summary>Demo videos</summary>


https://github.com/user-attachments/assets/476d992c-c6ca-4bcd-a3f2-b26cc612d1b9


https://github.com/user-attachments/assets/1c1a2537-de54-4db2-bdbf-6f1908ff1ce7


https://github.com/user-attachments/assets/9c992254-fc2b-402c-beec-20fceef25e6b


https://github.com/user-attachments/assets/d66abc1c-b8bf-45f8-a552-ec989dab310f
</details>

<!-- 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

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

---------

Signed-off-by: Shawn Yuan <shuaiyuan@microsoft.com>
Signed-off-by: Shuai Yuan <shuai.yuan.zju@gmail.com>
Co-authored-by: Niels Laute <niels.laute@live.nl>

src/settings-ui/Settings.UI/SettingsXAML/OOBE/Views/OobeWhatsNew.xaml.cs

@@ -4,6 +4,7 @@
 
 using System;
 using System.Collections.Generic;
+using System.ComponentModel;
 using System.Diagnostics;
 using System.Linq;
 using System.Net;
@@ -17,9 +18,11 @@ using CommunityToolkit.WinUI.UI.Controls;
 using global::PowerToys.GPOWrapper;
 using ManagedCommon;
 using Microsoft.PowerToys.Settings.UI.Helpers;
+using Microsoft.PowerToys.Settings.UI.Library.HotkeyConflicts;
 using Microsoft.PowerToys.Settings.UI.OOBE.Enums;
 using Microsoft.PowerToys.Settings.UI.OOBE.ViewModel;
 using Microsoft.PowerToys.Settings.UI.SerializationContext;
+using Microsoft.PowerToys.Settings.UI.Services;
 using Microsoft.PowerToys.Settings.UI.Views;
 using Microsoft.PowerToys.Telemetry;
 using Microsoft.UI.Xaml.Controls;
@@ -27,12 +30,54 @@ using Microsoft.UI.Xaml.Navigation;
 
 namespace Microsoft.PowerToys.Settings.UI.OOBE.Views
 {
-    public sealed partial class OobeWhatsNew : Page
+    public sealed partial class OobeWhatsNew : Page, INotifyPropertyChanged
     {
         public OobePowerToysModule ViewModel { get; set; }
 
+        private AllHotkeyConflictsData _allHotkeyConflictsData = new AllHotkeyConflictsData();
+
         public bool ShowDataDiagnosticsInfoBar => GetShowDataDiagnosticsInfoBar();
 
+        public AllHotkeyConflictsData AllHotkeyConflictsData
+        {
+            get => _allHotkeyConflictsData;
+            set
+            {
+                if (_allHotkeyConflictsData != value)
+                {
+                    _allHotkeyConflictsData = value;
+                    OnPropertyChanged(nameof(AllHotkeyConflictsData));
+                    OnPropertyChanged(nameof(HasConflicts));
+                }
+            }
+        }
+
+        public bool HasConflicts
+        {
+            get
+            {
+                if (AllHotkeyConflictsData == null)
+                {
+                    return false;
+                }
+
+                int count = 0;
+                if (AllHotkeyConflictsData.InAppConflicts != null)
+                {
+                    count += AllHotkeyConflictsData.InAppConflicts.Count;
+                }
+
+                if (AllHotkeyConflictsData.SystemConflicts != null)
+                {
+                    count += AllHotkeyConflictsData.SystemConflicts.Count;
+                }
+
+                return count > 0;
+            }
+        }
+
+        public event PropertyChangedEventHandler PropertyChanged;
+
         /// <summary>
         /// Initializes a new instance of the <see cref="OobeWhatsNew"/> class.
         /// </summary>
@@ -40,7 +85,27 @@ namespace Microsoft.PowerToys.Settings.UI.OOBE.Views
         {
             this.InitializeComponent();
             ViewModel = new OobePowerToysModule(OobeShellPage.OobeShellHandler.Modules[(int)PowerToysModules.WhatsNew]);
-            DataContext = ViewModel;
+            DataContext = this;
+
+            // Subscribe to hotkey conflict updates
+            if (GlobalHotkeyConflictManager.Instance != null)
+            {
+                GlobalHotkeyConflictManager.Instance.ConflictsUpdated += OnConflictsUpdated;
+                GlobalHotkeyConflictManager.Instance.RequestAllConflicts();
+            }
+        }
+
+        private void OnConflictsUpdated(object sender, AllHotkeyConflictsEventArgs e)
+        {
+            this.DispatcherQueue.TryEnqueue(Microsoft.UI.Dispatching.DispatcherQueuePriority.Normal, () =>
+            {
+                AllHotkeyConflictsData = e.Conflicts ?? new AllHotkeyConflictsData();
+            });
+        }
+
+        private void OnPropertyChanged(string propertyName)
+        {
+            PropertyChanged?.Invoke(this, new PropertyChangedEventArgs(propertyName));
         }
 
         private bool GetShowDataDiagnosticsInfoBar()
@@ -184,6 +249,12 @@ namespace Microsoft.PowerToys.Settings.UI.OOBE.Views
         protected override void OnNavigatedFrom(NavigationEventArgs e)
         {
             ViewModel.LogClosingModuleEvent();
+
+            // Unsubscribe from conflict updates when leaving the page
+            if (GlobalHotkeyConflictManager.Instance != null)
+            {
+                GlobalHotkeyConflictManager.Instance.ConflictsUpdated -= OnConflictsUpdated;
+            }
         }
 
         private void ReleaseNotesMarkdown_LinkClicked(object sender, LinkClickedEventArgs e)