Settings Flyout improvement (#43840)

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fix/what does it change/how was it tested (even manually, if necessary)?
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## Summary of the Pull Request
This pull request introduces the new Quick Access feature to PowerToys
by integrating its host process management into the runner and system
tray. The changes add the Quick Access host implementation, update
project and build files to include it, and modify the runner and tray
icon logic to launch and interact with the Quick Access UI.

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## PR Checklist

- [x] Closes: #43694
<!-- - [ ] Closes: #yyy (add separate lines for additional resolved
issues) -->
- [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
- [ ] **Localization:** All end-user-facing strings can be localized
- [ ] **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

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## Detailed Description of the Pull Request / Additional comments
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---------

Signed-off-by: Shawn Yuan (from Dev Box) <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/GeneralSettings.cs

@@ -7,6 +7,7 @@ using System.Text.Json;
 using System.Text.Json.Serialization;
 
 using ManagedCommon;
+using Microsoft.PowerToys.Settings.UI.Library.Helpers;
 using Microsoft.PowerToys.Settings.UI.Library.Interfaces;
 using Microsoft.PowerToys.Settings.UI.Library.Utilities;
 using Settings.UI.Library.Attributes;
@@ -19,7 +20,7 @@ namespace Microsoft.PowerToys.Settings.UI.Library
         ByStatus,
     }
 
-    public class GeneralSettings : ISettingsConfig
+    public class GeneralSettings : ISettingsConfig, IHotkeyConfig
     {
         // Gets or sets a value indicating whether run powertoys on start-up.
         [JsonPropertyName("startup")]
@@ -48,6 +49,14 @@ namespace Microsoft.PowerToys.Settings.UI.Library
         [JsonPropertyName("enable_warnings_elevated_apps")]
         public bool EnableWarningsElevatedApps { get; set; }
 
+        // Gets or sets a value indicating whether Quick Access is enabled.
+        [JsonPropertyName("enable_quick_access")]
+        public bool EnableQuickAccess { get; set; }
+
+        // Gets or sets Quick Access shortcut.
+        [JsonPropertyName("quick_access_shortcut")]
+        public HotkeySettings QuickAccessShortcut { get; set; }
+
         // Gets or sets theme Name.
         [JsonPropertyName("theme")]
         public string Theme { get; set; }
@@ -94,6 +103,8 @@ namespace Microsoft.PowerToys.Settings.UI.Library
             ShowSysTrayIcon = true;
             IsAdmin = false;
             EnableWarningsElevatedApps = true;
+            EnableQuickAccess = true;
+            QuickAccessShortcut = new HotkeySettings();
             IsElevated = false;
             ShowNewUpdatesToastNotification = true;
             AutoDownloadUpdates = false;
@@ -116,6 +127,22 @@ namespace Microsoft.PowerToys.Settings.UI.Library
             IgnoredConflictProperties = new ShortcutConflictProperties();
         }
 
+        public HotkeyAccessor[] GetAllHotkeyAccessors()
+        {
+            return new HotkeyAccessor[]
+            {
+                new HotkeyAccessor(
+                    () => QuickAccessShortcut,
+                    (hotkey) => { QuickAccessShortcut = hotkey; },
+                    "GeneralPage_QuickAccessShortcut"),
+            };
+        }
+
+        public ModuleType GetModuleType()
+        {
+            return ModuleType.GeneralSettings;
+        }
+
         // converts the current to a json string.
         public string ToJsonString()
         {