CmdPal: Treat System command provider as special (#43321)

## Summary of the Pull Request

This change marks the System command provider as special, ensuring
fallback items are surfaced at the top of the list.

Additionally, the SystemCommandExtensionProvider ID has been updated to
comply with the new naming convention.

As a small cleanup, SystemCommandExtensionProvider is now sealed.

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## PR Checklist

- [x] Related to: #42524
- [ ] **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
- [ ] **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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src/modules/cmdpal/Microsoft.CmdPal.UI.ViewModels/Commands/BuiltInsCommandProvider.cs

@@ -11,7 +11,7 @@ namespace Microsoft.CmdPal.UI.ViewModels.BuiltinCommands;
 /// <summary>
 /// Built-in Provider for a top-level command which can quit the application. Invokes the <see cref="QuitCommand"/>, which sends a <see cref="QuitMessage"/>.
 /// </summary>
-public partial class BuiltInsCommandProvider : CommandProvider
+public sealed partial class BuiltInsCommandProvider : CommandProvider
 {
     private readonly OpenSettingsCommand openSettings = new();
     private readonly QuitCommand quitCommand = new();
@@ -34,7 +34,7 @@ public partial class BuiltInsCommandProvider : CommandProvider
 
     public BuiltInsCommandProvider()
     {
-        Id = "Core";
+        Id = "com.microsoft.cmdpal.builtin.core";
         DisplayName = Properties.Resources.builtin_display_name;
         Icon = IconHelpers.FromRelativePath("Assets\\StoreLogo.scale-200.png");
     }

src/modules/cmdpal/Microsoft.CmdPal.UI.ViewModels/Commands/MainListPage.cs

@@ -30,7 +30,12 @@ public partial class MainListPage : DynamicListPage,
 {
     private readonly string[] _specialFallbacks = [
         "com.microsoft.cmdpal.builtin.run",
-        "com.microsoft.cmdpal.builtin.calculator"
+        "com.microsoft.cmdpal.builtin.calculator",
+        "com.microsoft.cmdpal.builtin.system",
+        "com.microsoft.cmdpal.builtin.core",
+        "com.microsoft.cmdpal.builtin.websearch",
+        "com.microsoft.cmdpal.builtin.windowssettings",
+        "com.microsoft.cmdpal.builtin.datetime",
     ];
 
     private readonly IServiceProvider _serviceProvider;