Introduce new utility PowerDisplay to control your monitor settings (#42642)

<!-- 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
Introduce a new PowerToys' module PowerDisplay to let user can control
their monitor settings without touching monitor's button.

Support feature list:
Common:
1. Profiles support
2. Integration with LightSwitch (auto switch profile when theme change)
3. TrayIcon
4. Save and restore settings when startup
5. Shortcut
6. Rotation
7. GPO support
8. Auto re-discovery monitor when plugging and unplugging monitors.
9. Identify Monitors
10. Quick profile switch

Especially for DDC/CI monitor:
1. Brightness
2. Contrast
3. Volume
4. Color temperature (preset profile)
5. Input source
6. Power State (poweroff)


Design doc:
https://github.com/microsoft/PowerToys/blob/yuleng/display/pr/3/doc/devdocs/modules/powerdisplay/design.md

AOT compatibility:
I designed this module for AOT from the start, so I'm pretty sure at
least 95% of it is AOT compatible. But unfortunately, PowerToys still
have a AOT blocker to block this module publish with AOT.

Currently PowerToys will check the .net file version (file version not
lib version) to avoid crash. So, all modules should reference Common.UI
or add UseWPF to avoid overwrite the .net file with different version
(which may cause crash).

Todo:
- [ ] BugBash
- [ ] Icon
- [ ] IdentifyWindow UI improvement


Demo

Main UI:
<img width="546" height="671" alt="image"
src="https://github.com/user-attachments/assets/b0ad9ac5-8000-4365-a192-ab8c2d66d4f1"
/>

Input Source:
<img width="536" height="674" alt="image"
src="https://github.com/user-attachments/assets/80f9ccd7-4f8c-4201-b177-cc86c5bcc9e3"
/>


Settings UI:
<img width="1581" height="1191" alt="image"
src="https://github.com/user-attachments/assets/6a82e4bb-8f96-4f28-abf9-d7c45e1c8ef7"
/>

<img width="1525" height="1146" alt="image"
src="https://github.com/user-attachments/assets/aae81e65-08fd-453a-bf52-02a74f2fdea0"
/>



Closes: 
#42942
#42678
#41117
#38109
#35564
#34932
#28500
#1052
#18149

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## PR Checklist

- [x] Closes: #1052
- [x] **Communication:** I've discussed this with core contributors
already. If the work hasn't been agreed, this work might be rejected
- [x] **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)
- [ ] **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: #xxx

<!-- 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

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---------

Co-authored-by: Yu Leng <yuleng@microsoft.com>
Co-authored-by: Niels Laute <niels.laute@live.nl>
Co-authored-by: moooyo <lengyuchn@gmail.com>
Co-authored-by: Copilot <198982749+Copilot@users.noreply.github.com>
Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>
Co-authored-by: Claude Opus 4.5 <noreply@anthropic.com>

src/settings-ui/Settings.UI.Library/PowerDisplayProperties.cs

@@ -0,0 +1,65 @@
+// 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.Collections.Generic;
+using System.Text.Json.Serialization;
+using PowerDisplay.Common.Models;
+using Settings.UI.Library.Attributes;
+
+namespace Microsoft.PowerToys.Settings.UI.Library
+{
+    public class PowerDisplayProperties
+    {
+        [CmdConfigureIgnore]
+        public HotkeySettings DefaultActivationShortcut => new HotkeySettings(true, true, false, true, 0x44); // Ctrl+Shift+Win+D (win, ctrl, alt, shift, code)
+
+        public PowerDisplayProperties()
+        {
+            ActivationShortcut = DefaultActivationShortcut;
+            MonitorRefreshDelay = 5;
+            Monitors = new List<MonitorInfo>();
+            RestoreSettingsOnStartup = false;
+            ShowSystemTrayIcon = true;
+            ShowProfileSwitcher = true;
+            ShowIdentifyMonitorsButton = true;
+
+            // Note: saved_monitor_settings has been moved to monitor_state.json
+            // which is managed separately by PowerDisplay app
+        }
+
+        [JsonPropertyName("activation_shortcut")]
+        public HotkeySettings ActivationShortcut { get; set; }
+
+        /// <summary>
+        /// Gets or sets delay in seconds before refreshing monitors after display changes (hot-plug).
+        /// This allows hardware to stabilize before querying DDC/CI.
+        /// </summary>
+        [JsonPropertyName("monitor_refresh_delay")]
+        public int MonitorRefreshDelay { get; set; }
+
+        [JsonPropertyName("monitors")]
+        public List<MonitorInfo> Monitors { get; set; }
+
+        [JsonPropertyName("restore_settings_on_startup")]
+        public bool RestoreSettingsOnStartup { get; set; }
+
+        [JsonPropertyName("show_system_tray_icon")]
+        public bool ShowSystemTrayIcon { get; set; }
+
+        /// <summary>
+        /// Gets or sets whether to show the profile switcher button in the flyout UI.
+        /// Default is true. When false, the profile switcher is hidden (but profiles still work via Settings).
+        /// Note: Also hidden when no profiles exist.
+        /// </summary>
+        [JsonPropertyName("show_profile_switcher")]
+        public bool ShowProfileSwitcher { get; set; }
+
+        /// <summary>
+        /// Gets or sets whether to show the identify monitors button in the flyout UI.
+        /// Default is true.
+        /// </summary>
+        [JsonPropertyName("show_identify_monitors_button")]
+        public bool ShowIdentifyMonitorsButton { get; set; }
+    }
+}