[Settings] Create a global static instance of SettingsUtils (#44064)

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## Summary of the Pull Request

SettingsUtils is initialized multiple times over the whole solution.
This creates one singeltone instance (with the default settings), so it
only has to be initialized once (and improve performance a bit with
that)

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## PR Checklist

- [ ] Closes: #xxx
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- [ ] **Communication:** I've discussed this with core contributors
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- [ ] **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
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## Detailed Description of the Pull Request / Additional comments

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## Validation Steps Performed

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

@@ -22,7 +22,14 @@ namespace Microsoft.PowerToys.Settings.UI.Library
         private readonly ISettingsPath _settingsPath;
         private readonly JsonSerializerOptions _serializerOptions;
 
-        public SettingsUtils()
+        /// <summary>
+        /// Gets the default instance of the <see cref="SettingsUtils"/> class for general use.
+        /// Same as instantiating a new instance with the <see cref="SettingsUtils(IFileSystem?, JsonSerializerOptions?)"/> constructor with a new <see cref="FileSystem"/> object as the first argument and <c>null</c> as the second argument.
+        /// </summary>
+        /// <remarks>For using in tests, you should use one of the public constructors.</remarks>
+        public static SettingsUtils Default { get; } = new SettingsUtils();
+
+        private SettingsUtils()
             : this(new FileSystem())
         {
         }
@@ -234,7 +241,7 @@ namespace Microsoft.PowerToys.Settings.UI.Library
         public static (bool Success, string Message, string Severity, bool LastBackupExists, string OptionalMessage) BackupSettings()
         {
             var settingsBackupAndRestoreUtilsX = SettingsBackupAndRestoreUtils.Instance;
-            var settingsUtils = new SettingsUtils();
+            var settingsUtils = Default;
             var appBasePath = Path.GetDirectoryName(settingsUtils._settingsPath.GetSettingsPath(string.Empty, string.Empty));
             string settingsBackupAndRestoreDir = settingsBackupAndRestoreUtilsX.GetSettingsBackupAndRestoreDir();
 
@@ -247,7 +254,7 @@ namespace Microsoft.PowerToys.Settings.UI.Library
         public static (bool Success, string Message, string Severity) RestoreSettings()
         {
             var settingsBackupAndRestoreUtilsX = SettingsBackupAndRestoreUtils.Instance;
-            var settingsUtils = new SettingsUtils();
+            var settingsUtils = Default;
             var appBasePath = Path.GetDirectoryName(settingsUtils._settingsPath.GetSettingsPath(string.Empty, string.Empty));
             string settingsBackupAndRestoreDir = settingsBackupAndRestoreUtilsX.GetSettingsBackupAndRestoreDir();
             return settingsBackupAndRestoreUtilsX.RestoreSettings(appBasePath, settingsBackupAndRestoreDir);