[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/Helpers/HotkeyConflictHelper.cs

@@ -0,0 +1,73 @@
+// 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.Text.Json.Nodes;
+using Microsoft.PowerToys.Settings.UI.Library;
+
+namespace Microsoft.PowerToys.Settings.UI.Helpers
+{
+    public class HotkeyConflictHelper
+    {
+        public delegate void HotkeyConflictCheckCallback(bool hasConflict, HotkeyConflictResponse conflicts);
+
+        private static readonly Dictionary<string, HotkeyConflictCheckCallback> PendingHotkeyConflictChecks = new Dictionary<string, HotkeyConflictCheckCallback>();
+        private static readonly object LockObject = new object();
+
+        public static void CheckHotkeyConflict(HotkeySettings hotkeySettings, Func<string, int> ipcMSGCallBackFunc, HotkeyConflictCheckCallback callback)
+        {
+            if (hotkeySettings == null || ipcMSGCallBackFunc == null)
+            {
+                return;
+            }
+
+            string requestId = GenerateRequestId();
+
+            lock (LockObject)
+            {
+                PendingHotkeyConflictChecks[requestId] = callback;
+            }
+
+            var hotkeyObj = new JsonObject
+            {
+                ["request_id"] = requestId,
+                ["win"] = hotkeySettings.Win,
+                ["ctrl"] = hotkeySettings.Ctrl,
+                ["shift"] = hotkeySettings.Shift,
+                ["alt"] = hotkeySettings.Alt,
+                ["key"] = hotkeySettings.Code,
+            };
+
+            var requestObject = new JsonObject
+            {
+                ["check_hotkey_conflict"] = hotkeyObj,
+            };
+
+            ipcMSGCallBackFunc(requestObject.ToString());
+        }
+
+        public static void HandleHotkeyConflictResponse(HotkeyConflictResponse response)
+        {
+            if (response.AllConflicts.Count == 0)
+            {
+                return;
+            }
+
+            HotkeyConflictCheckCallback callback = null;
+
+            lock (LockObject)
+            {
+                if (PendingHotkeyConflictChecks.TryGetValue(response.RequestId, out callback))
+                {
+                    PendingHotkeyConflictChecks.Remove(response.RequestId);
+                }
+            }
+
+            callback?.Invoke(response.HasConflict, response);
+        }
+
+        private static string GenerateRequestId() => Guid.NewGuid().ToString();
+    }
+}

src/settings-ui/Settings.UI/Helpers/HotkeyConflictResponse.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;
+using Microsoft.PowerToys.Settings.UI.Library.HotkeyConflicts;
+
+namespace Microsoft.PowerToys.Settings.UI.Helpers
+{
+    public class HotkeyConflictResponse
+    {
+        public string RequestId { get; set; }
+
+        public bool HasConflict { get; set; }
+
+        public List<ModuleHotkeyData> AllConflicts { get; set; } = new List<ModuleHotkeyData>();
+    }
+}