[Settings, Common.UI, runner exe] Unify exe/dll naming (#15005)

* Unify exe/dll naming - PowerToys.Runner

Align naming with other exes - PowerToys Runner -> PowerToys.Runner

* Unify exe/dll naming - Microsoft.PowerToys.Common.UI

Project name - Microsoft.PowerToys.Common.UI -> Common.UI
dll name - Microsoft.PowerToys.Common.UI.dll -> PowerToys.Common.UI.dll

* Unify exe/dll naming - Settings

Project names - Microsoft.PowerToys.Settings* -> Settings*
Dll names - Microsoft.PowerToys.Settings*.dll -> PowerToys.Settings*.dll

* Revert file autoformat

* [Docs] Update paths to settings projects/files

* Fix tests - Update path

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

@@ -0,0 +1,57 @@
+// 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;
+using System.Text.Json.Serialization;
+using Microsoft.PowerToys.Settings.UI.Library.Interfaces;
+
+namespace Microsoft.PowerToys.Settings.UI.Library
+{
+    public class PowerLauncherSettings : BasePTModuleSettings, ISettingsConfig
+    {
+        public const string ModuleName = "PowerToys Run";
+
+        [JsonPropertyName("properties")]
+        public PowerLauncherProperties Properties { get; set; }
+
+        [JsonPropertyName("plugins")]
+        public IEnumerable<PowerLauncherPluginSettings> Plugins { get; set; } = new List<PowerLauncherPluginSettings>();
+
+        public PowerLauncherSettings()
+        {
+            Properties = new PowerLauncherProperties();
+            Version = "1.0";
+            Name = ModuleName;
+        }
+
+        public virtual void Save(ISettingsUtils settingsUtils)
+        {
+            // Save settings to file
+            var options = new JsonSerializerOptions
+            {
+                WriteIndented = true,
+            };
+
+            if (settingsUtils == null)
+            {
+                throw new ArgumentNullException(nameof(settingsUtils));
+            }
+
+            settingsUtils.SaveSettings(JsonSerializer.Serialize(this, options), ModuleName);
+        }
+
+        public string GetModuleName()
+        {
+            return Name;
+        }
+
+        // This can be utilized in the future if the settings.json file is to be modified/deleted.
+        public bool UpgradeSettingsConfiguration()
+        {
+            return false;
+        }
+    }
+}