[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/ViewModels/PowerOcrViewModel.cs

@@ -11,6 +11,7 @@ using System.Text.Json;
 using System.Timers;
 using global::PowerToys.GPOWrapper;
 using ManagedCommon;
+using Microsoft.PowerToys.Settings.UI.Helpers;
 using Microsoft.PowerToys.Settings.UI.Library;
 using Microsoft.PowerToys.Settings.UI.Library.Helpers;
 using Microsoft.PowerToys.Settings.UI.Library.Interfaces;
@@ -20,9 +21,11 @@ using Windows.Media.Ocr;
 
 namespace Microsoft.PowerToys.Settings.UI.ViewModels
 {
-    public partial class PowerOcrViewModel : Observable, IDisposable
+    public partial class PowerOcrViewModel : PageViewModelBase
     {
-        private bool disposedValue;
+        protected override string ModuleName => PowerOcrSettings.ModuleName;
+
+        private bool _disposed;
 
         // Delay saving of settings in order to avoid calling save multiple times and hitting file in use exception. If there is no other request to save settings in given interval, we proceed to save it; otherwise, we schedule saving it after this interval
         private const int SaveSettingsDelayInMs = 500;
@@ -114,6 +117,16 @@ namespace Microsoft.PowerToys.Settings.UI.ViewModels
             }
         }
 
+        public override Dictionary<string, HotkeySettings[]> GetAllHotkeySettings()
+        {
+            var hotkeysDict = new Dictionary<string, HotkeySettings[]>
+            {
+                [ModuleName] = [ActivationShortcut],
+            };
+
+            return hotkeysDict;
+        }
+
         public bool IsEnabled
         {
             get => _isEnabled;
@@ -246,23 +259,20 @@ namespace Microsoft.PowerToys.Settings.UI.ViewModels
             OnPropertyChanged(nameof(IsEnabled));
         }
 
-        protected virtual void Dispose(bool disposing)
+        protected override void Dispose(bool disposing)
         {
-            if (!disposedValue)
+            if (!_disposed)
             {
                 if (disposing)
                 {
-                    _delayedTimer.Dispose();
+                    _delayedTimer?.Dispose();
+                    _delayedTimer = null;
                 }
 
-                disposedValue = true;
+                _disposed = true;
             }
-        }
 
-        public void Dispose()
-        {
-            Dispose(disposing: true);
-            GC.SuppressFinalize(this);
+            base.Dispose(disposing);
         }
 
         public string SnippingToolInfoBarMargin