CmdPal: Add precomputed fuzzy string matching to Command Palette (#44090)

## Summary of the Pull Request

This PR improves fuzzy matching in Command Palette by:
- Precomputing normalized strings to enable faster comparisons
- Reducing memory allocations during matching, effectively down to zero

It also introduces several behavioral improvements:
- Strips diacritics from the normalized search string to improve
matching across languages
- Suppresses the same-case bonus when the query consists entirely of
lowercase characters -- reflecting typical user input patterns
- Allows skipping word separators -- enabling queries like Power Point
to match PowerPoint

This implementation is currently kept internal and is used only on the
home page. For other scenarios, the `FuzzyStringMatcher` from
`Microsoft.CommandPalette.Extensions.Toolkit` is being improved instead.

`PrecomputedFuzzyMatcher` offers up to a 100× performance improvement
over the current `FuzzyStringMatcher`, and approximately 2–5× better
performance compared to the improved version.

The improvement might seem small, but it adds up and becomes quite
noticeable when filtering the entire home page—whether the user starts a
new search or changes the query non-incrementally (e.g., using
backspace).


<!-- Please review the items on the PR checklist before submitting-->
## PR Checklist

- [x] Closes: #45226
- [x] Closes: #44066
- [ ] **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

<!-- 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

<!-- Describe how you validated the behavior. Add automated tests
wherever possible, but list manual validation steps taken as well -->
## Validation Steps Performed

src/modules/cmdpal/Microsoft.CmdPal.UI/App.xaml.cs

@@ -6,6 +6,7 @@ using ManagedCommon;
 using Microsoft.CmdPal.Core.Common;
 using Microsoft.CmdPal.Core.Common.Helpers;
 using Microsoft.CmdPal.Core.Common.Services;
+using Microsoft.CmdPal.Core.Common.Text;
 using Microsoft.CmdPal.Core.ViewModels;
 using Microsoft.CmdPal.Ext.Apps;
 using Microsoft.CmdPal.Ext.Bookmarks;
@@ -206,6 +207,9 @@ public partial class App : Application, IDisposable
         services.AddSingleton<IAppHostService, PowerToysAppHostService>();
         services.AddSingleton<ITelemetryService, TelemetryForwarder>();
 
+        services.AddSingleton<IFuzzyMatcherProvider, FuzzyMatcherProvider>(
+            _ => new FuzzyMatcherProvider(new PrecomputedFuzzyMatcherOptions(), new PinyinFuzzyMatcherOptions()));
+
         // ViewModels
         services.AddSingleton<ShellViewModel>();
         services.AddSingleton<IPageViewModelFactoryService, CommandPalettePageViewModelFactory>();

src/modules/cmdpal/Microsoft.CmdPal.UI/Controls/ContextMenu.xaml.cs

@@ -4,9 +4,11 @@
 
 using CommunityToolkit.Mvvm.Messaging;
 using CommunityToolkit.WinUI;
+using Microsoft.CmdPal.Core.Common.Text;
 using Microsoft.CmdPal.Core.ViewModels;
 using Microsoft.CmdPal.Core.ViewModels.Messages;
 using Microsoft.CmdPal.UI.Messages;
+using Microsoft.Extensions.DependencyInjection;
 using Microsoft.UI.Input;
 using Microsoft.UI.Xaml;
 using Microsoft.UI.Xaml.Controls;
@@ -21,21 +23,19 @@ public sealed partial class ContextMenu : UserControl,
     IRecipient<UpdateCommandBarMessage>,
     IRecipient<TryCommandKeybindingMessage>
 {
-    public ContextMenuViewModel ViewModel { get; } = new();
+    public ContextMenuViewModel ViewModel { get; }
 
     public ContextMenu()
     {
         this.InitializeComponent();
 
+        ViewModel = new ContextMenuViewModel(App.Current.Services.GetRequiredService<IFuzzyMatcherProvider>());
+        ViewModel.PropertyChanged += ViewModel_PropertyChanged;
+
         // RegisterAll isn't AOT compatible
         WeakReferenceMessenger.Default.Register<OpenContextMenuMessage>(this);
         WeakReferenceMessenger.Default.Register<UpdateCommandBarMessage>(this);
         WeakReferenceMessenger.Default.Register<TryCommandKeybindingMessage>(this);
-
-        if (ViewModel is not null)
-        {
-            ViewModel.PropertyChanged += ViewModel_PropertyChanged;
-        }
     }
 
     public void Receive(OpenContextMenuMessage message)

src/modules/cmdpal/Microsoft.CmdPal.UI/PowerToysRootPageService.cs

@@ -6,6 +6,7 @@ using System.Runtime.InteropServices;
 using System.Runtime.Versioning;
 using ManagedCommon;
 using Microsoft.CmdPal.Core.Common.Services;
+using Microsoft.CmdPal.Core.Common.Text;
 using Microsoft.CmdPal.Core.ViewModels;
 using Microsoft.CmdPal.UI.ViewModels;
 using Microsoft.CmdPal.UI.ViewModels.MainPage;
@@ -23,13 +24,13 @@ internal sealed class PowerToysRootPageService : IRootPageService
     private IExtensionWrapper? _activeExtension;
     private Lazy<MainListPage> _mainListPage;
 
-    public PowerToysRootPageService(TopLevelCommandManager topLevelCommandManager, SettingsModel settings, AliasManager aliasManager, AppStateModel appStateModel)
+    public PowerToysRootPageService(TopLevelCommandManager topLevelCommandManager, SettingsModel settings, AliasManager aliasManager, AppStateModel appStateModel, IFuzzyMatcherProvider fuzzyMatcherProvider)
     {
         _tlcManager = topLevelCommandManager;
 
         _mainListPage = new Lazy<MainListPage>(() =>
         {
-            return new MainListPage(_tlcManager, settings, aliasManager, appStateModel);
+            return new MainListPage(_tlcManager, settings, aliasManager, appStateModel, fuzzyMatcherProvider);
         });
     }