[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.UnitTests/ViewModelTests/PowerLauncherViewModelTest.cs

@@ -3,8 +3,8 @@
 // See the LICENSE file in the project root for more information.
 
 using System;
-
 using Microsoft.PowerToys.Settings.UI.Library;
+using Microsoft.PowerToys.Settings.UI.Library.Interfaces;
 using Microsoft.PowerToys.Settings.UI.UnitTests.BackwardsCompatibility;
 using Microsoft.PowerToys.Settings.UI.ViewModels;
 using Microsoft.VisualStudio.TestTools.UnitTesting;
@@ -13,7 +13,7 @@ using Moq;
 namespace ViewModelTests
 {
     [TestClass]
-    public class PowerLauncherViewModelTest
+    public class PowerLauncherViewModelTest : IDisposable
     {
         private sealed class SendCallbackMock
         {
@@ -26,20 +26,48 @@ namespace ViewModelTests
             {
                 TimesSent++;
             }
+
+            [System.Diagnostics.CodeAnalysis.SuppressMessage("StyleCop.CSharp.NamingRules", "SA1313:Parameter names should begin with lower-case letter", Justification = "We actually don't validate setting, just calculate it was sent")]
+            public int OnSendIPC(string _)
+            {
+                TimesSent++;
+                return 0;
+            }
         }
 
         private PowerLauncherViewModel viewModel;
         private PowerLauncherSettings mockSettings;
         private SendCallbackMock sendCallbackMock;
+        private BackCompatTestProperties.MockSettingsRepository<GeneralSettings> mockGeneralSettingsRepository;
 
         [TestInitialize]
         public void Initialize()
         {
             mockSettings = new PowerLauncherSettings();
             sendCallbackMock = new SendCallbackMock();
+
+            var settingPathMock = new Mock<ISettingsPath>();
+            var mockGeneralIOProvider = BackCompatTestProperties.GetGeneralSettingsIOProvider("v0.22.0");
+            var mockGeneralSettingsUtils = new SettingsUtils(mockGeneralIOProvider.Object, settingPathMock.Object);
+            mockGeneralSettingsRepository = new BackCompatTestProperties.MockSettingsRepository<GeneralSettings>(mockGeneralSettingsUtils);
+
             viewModel = new PowerLauncherViewModel(
                 mockSettings,
-                new PowerLauncherViewModel.SendCallback(sendCallbackMock.OnSend));
+                mockGeneralSettingsRepository,
+                sendCallbackMock.OnSendIPC,
+                () => false);
+        }
+
+        [TestCleanup]
+        public void Cleanup()
+        {
+            viewModel?.Dispose();
+        }
+
+        public void Dispose()
+        {
+            viewModel?.Dispose();
+            GC.SuppressFinalize(this);
         }
 
         /// <summary>
@@ -67,7 +95,7 @@ namespace ViewModelTests
 
             // Initialise View Model with test Config files
             Func<string, int> sendMockIPCConfigMSG = msg => { return 0; };
-            PowerLauncherViewModel viewModel = new PowerLauncherViewModel(originalSettings, generalSettingsRepository, sendMockIPCConfigMSG, () => true);
+            using PowerLauncherViewModel viewModel = new PowerLauncherViewModel(originalSettings, generalSettingsRepository, sendMockIPCConfigMSG, () => true);
 
             // Verify that the old settings persisted
             Assert.AreEqual(originalGeneralSettings.Enabled.PowerLauncher, viewModel.EnablePowerLauncher);