[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/runner/settings_window.cpp

@@ -13,6 +13,7 @@
 #include "UpdateUtils.h"
 #include "centralized_kb_hook.h"
 #include "Generated files/resource.h"
+#include "hotkey_conflict_detector.h"
 
 #include <common/utils/json.h>
 #include <common/SettingsAPI/settings_helpers.cpp>
@@ -153,6 +154,8 @@ void send_json_config_to_module(const std::wstring& module_key, const std::wstri
     if (moduleIt != modules().end())
     {
         moduleIt->second->set_config(settings.c_str());
+
+        moduleIt->second.remove_hotkey_records();
         moduleIt->second.update_hotkeys();
         moduleIt->second.UpdateHotkeyEx();
     }
@@ -249,6 +252,77 @@ void dispatch_received_json(const std::wstring& json_to_parse)
             const std::wstring save_file_location = PTSettingsHelper::get_root_save_folder_location() + language_filename;
             json::to_file(save_file_location, j);
         }
+        else if (name == L"check_hotkey_conflict")
+        {
+            try
+            {
+                PowertoyModuleIface::Hotkey hotkey;
+                hotkey.win = value.GetObjectW().GetNamedBoolean(L"win", false);
+                hotkey.ctrl = value.GetObjectW().GetNamedBoolean(L"ctrl", false);
+                hotkey.shift = value.GetObjectW().GetNamedBoolean(L"shift", false);
+                hotkey.alt = value.GetObjectW().GetNamedBoolean(L"alt", false);
+                hotkey.key = static_cast<unsigned char>(value.GetObjectW().GetNamedNumber(L"key", 0));
+
+                std::wstring requestId = value.GetObjectW().GetNamedString(L"request_id", L"").c_str();
+
+                auto& hkmng = HotkeyConflictDetector::HotkeyConflictManager::GetInstance();
+                bool hasConflict = hkmng.HasConflict(hotkey);
+
+                json::JsonObject response;
+                response.SetNamedValue(L"response_type", json::JsonValue::CreateStringValue(L"hotkey_conflict_result"));
+                response.SetNamedValue(L"request_id", json::JsonValue::CreateStringValue(requestId));
+                response.SetNamedValue(L"has_conflict", json::JsonValue::CreateBooleanValue(hasConflict));
+
+                if (hasConflict)
+                {
+                    auto conflicts = hkmng.GetAllConflicts(hotkey);
+                    if (!conflicts.empty())
+                    {
+                        // Include all conflicts in the response
+                        json::JsonArray allConflicts;
+                        for (const auto& conflict : conflicts)
+                        {
+                            json::JsonObject conflictObj;
+                            conflictObj.SetNamedValue(L"module", json::JsonValue::CreateStringValue(conflict.moduleName));
+                            conflictObj.SetNamedValue(L"hotkeyID", json::JsonValue::CreateNumberValue(conflict.hotkeyID));
+                            allConflicts.Append(conflictObj);
+                        }
+                        response.SetNamedValue(L"all_conflicts", allConflicts);
+                    }
+                }
+
+                std::unique_lock lock{ ipc_mutex };
+                if (current_settings_ipc)
+                {
+                    current_settings_ipc->send(response.Stringify().c_str());
+                }
+            }
+            catch (...)
+            {
+                Logger::error(L"Failed to process hotkey conflict check request");
+            }
+        }
+        else if (name == L"get_all_hotkey_conflicts")
+        {
+            try
+            {
+                auto& hkmng = HotkeyConflictDetector::HotkeyConflictManager::GetInstance();
+                auto conflictsJson = hkmng.GetHotkeyConflictsAsJson();
+
+                // Add response type identifier
+                conflictsJson.SetNamedValue(L"response_type", json::JsonValue::CreateStringValue(L"all_hotkey_conflicts"));
+
+                std::unique_lock lock{ ipc_mutex };
+                if (current_settings_ipc)
+                {
+                    current_settings_ipc->send(conflictsJson.Stringify().c_str());
+                }
+            }
+            catch (...)
+            {
+                Logger::error(L"Failed to process get all hotkey conflicts request");
+            }
+        }
     }
     return;
 }