[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.Library/HotkeyConflicts/AllHotkeyConflictsData.cs

@@ -0,0 +1,19 @@
+// Copyright (c) Microsoft Corporation
+// The Microsoft Corporation licenses this file to you under the MIT license.
+// See the LICENSE file in the project root for more information.
+
+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Text;
+using System.Threading.Tasks;
+
+namespace Microsoft.PowerToys.Settings.UI.Library.HotkeyConflicts
+{
+    public class AllHotkeyConflictsData
+    {
+        public List<HotkeyConflictGroupData> InAppConflicts { get; set; } = new List<HotkeyConflictGroupData>();
+
+        public List<HotkeyConflictGroupData> SystemConflicts { get; set; } = new List<HotkeyConflictGroupData>();
+    }
+}

src/settings-ui/Settings.UI.Library/HotkeyConflicts/AllHotkeyConflictsEventArgs.cs

@@ -0,0 +1,22 @@
+// Copyright (c) Microsoft Corporation
+// The Microsoft Corporation licenses this file to you under the MIT license.
+// See the LICENSE file in the project root for more information.
+
+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Text;
+using System.Threading.Tasks;
+
+namespace Microsoft.PowerToys.Settings.UI.Library.HotkeyConflicts
+{
+    public class AllHotkeyConflictsEventArgs : EventArgs
+    {
+        public AllHotkeyConflictsData Conflicts { get; }
+
+        public AllHotkeyConflictsEventArgs(AllHotkeyConflictsData conflicts)
+        {
+            Conflicts = conflicts;
+        }
+    }
+}

src/settings-ui/Settings.UI.Library/HotkeyConflicts/HotkeyConflictGroupData.cs

@@ -0,0 +1,21 @@
+// Copyright (c) Microsoft Corporation
+// The Microsoft Corporation licenses this file to you under the MIT license.
+// See the LICENSE file in the project root for more information.
+
+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Text;
+using System.Threading.Tasks;
+
+namespace Microsoft.PowerToys.Settings.UI.Library.HotkeyConflicts
+{
+    public class HotkeyConflictGroupData
+    {
+        public HotkeyData Hotkey { get; set; }
+
+        public bool IsSystemConflict { get; set; }
+
+        public List<ModuleHotkeyData> Modules { get; set; }
+    }
+}

src/settings-ui/Settings.UI.Library/HotkeyConflicts/HotkeyConflictInfo.cs

@@ -0,0 +1,23 @@
+// Copyright (c) Microsoft Corporation
+// The Microsoft Corporation licenses this file to you under the MIT license.
+// See the LICENSE file in the project root for more information.
+
+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Text;
+using System.Threading.Tasks;
+
+namespace Microsoft.PowerToys.Settings.UI.Library.HotkeyConflicts
+{
+    public class HotkeyConflictInfo
+    {
+        public bool IsSystemConflict { get; set; }
+
+        public string ConflictingModuleName { get; set; }
+
+        public int ConflictingHotkeyID { get; set; }
+
+        public List<string> AllConflictingModules { get; set; } = new List<string>();
+    }
+}

src/settings-ui/Settings.UI.Library/HotkeyConflicts/HotkeyData.cs

@@ -0,0 +1,71 @@
+// Copyright (c) Microsoft Corporation
+// The Microsoft Corporation licenses this file to you under the MIT license.
+// See the LICENSE file in the project root for more information.
+
+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Text;
+using System.Threading.Tasks;
+using Microsoft.PowerToys.Settings.UI.Library.Utilities;
+
+namespace Microsoft.PowerToys.Settings.UI.Library.HotkeyConflicts
+{
+    public class HotkeyData
+    {
+        public bool Win { get; set; }
+
+        public bool Ctrl { get; set; }
+
+        public bool Shift { get; set; }
+
+        public bool Alt { get; set; }
+
+        public int Key { get; set; }
+
+        public List<object> GetKeysList()
+        {
+            List<object> shortcutList = new List<object>();
+
+            if (Win)
+            {
+                shortcutList.Add(92); // The Windows key or button.
+            }
+
+            if (Ctrl)
+            {
+                shortcutList.Add("Ctrl");
+            }
+
+            if (Alt)
+            {
+                shortcutList.Add("Alt");
+            }
+
+            if (Shift)
+            {
+                shortcutList.Add(16); // The Shift key or button.
+            }
+
+            if (Key > 0)
+            {
+                switch (Key)
+                {
+                    // https://learn.microsoft.com/uwp/api/windows.system.virtualkey?view=winrt-20348
+                    case 38: // The Up Arrow key or button.
+                    case 40: // The Down Arrow key or button.
+                    case 37: // The Left Arrow key or button.
+                    case 39: // The Right Arrow key or button.
+                        shortcutList.Add(Key);
+                        break;
+                    default:
+                        var localKey = Helper.GetKeyName((uint)Key);
+                        shortcutList.Add(localKey);
+                        break;
+                }
+            }
+
+            return shortcutList;
+        }
+    }
+}

src/settings-ui/Settings.UI.Library/HotkeyConflicts/ModuleConflictsData.cs

@@ -0,0 +1,21 @@
+// Copyright (c) Microsoft Corporation
+// The Microsoft Corporation licenses this file to you under the MIT license.
+// See the LICENSE file in the project root for more information.
+
+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Text;
+using System.Threading.Tasks;
+
+namespace Microsoft.PowerToys.Settings.UI.Library.HotkeyConflicts
+{
+    public class ModuleConflictsData
+    {
+        public List<HotkeyConflictGroupData> InAppConflicts { get; set; } = new List<HotkeyConflictGroupData>();
+
+        public List<HotkeyConflictGroupData> SystemConflicts { get; set; } = new List<HotkeyConflictGroupData>();
+
+        public bool HasConflicts => InAppConflicts.Count > 0 || SystemConflicts.Count > 0;
+    }
+}

src/settings-ui/Settings.UI.Library/HotkeyConflicts/ModuleHotkeyData.cs

@@ -0,0 +1,84 @@
+// Copyright (c) Microsoft Corporation
+// The Microsoft Corporation licenses this file to you under the MIT license.
+// See the LICENSE file in the project root for more information.
+
+using System.ComponentModel;
+using System.Runtime.CompilerServices;
+using ManagedCommon;
+using Microsoft.PowerToys.Settings.UI.Library.Helpers;
+using Windows.Web.AtomPub;
+
+namespace Microsoft.PowerToys.Settings.UI.Library.HotkeyConflicts
+{
+    public class ModuleHotkeyData : INotifyPropertyChanged
+    {
+        private string _moduleName;
+        private int _hotkeyID;
+        private HotkeySettings _hotkeySettings;
+        private bool _isSystemConflict;
+
+        public event PropertyChangedEventHandler PropertyChanged;
+
+        public string IconPath { get; set; }
+
+        public string DisplayName { get; set; }
+
+        public string Header { get; set; }
+
+        protected virtual void OnPropertyChanged([CallerMemberName] string propertyName = null)
+        {
+            PropertyChanged?.Invoke(this, new PropertyChangedEventArgs(propertyName));
+        }
+
+        public string ModuleName
+        {
+            get => _moduleName;
+            set
+            {
+                if (_moduleName != value)
+                {
+                    _moduleName = value;
+                }
+            }
+        }
+
+        public int HotkeyID
+        {
+            get => _hotkeyID;
+            set
+            {
+                if (_hotkeyID != value)
+                {
+                    _hotkeyID = value;
+                }
+            }
+        }
+
+        public HotkeySettings HotkeySettings
+        {
+            get => _hotkeySettings;
+            set
+            {
+                if (_hotkeySettings != value)
+                {
+                    _hotkeySettings = value;
+                    OnPropertyChanged();
+                }
+            }
+        }
+
+        public bool IsSystemConflict
+        {
+            get => _isSystemConflict;
+            set
+            {
+                if (_isSystemConflict != value)
+                {
+                    _isSystemConflict = value;
+                }
+            }
+        }
+
+        public ModuleType ModuleType { get; set; }
+    }
+}