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/Tests/Microsoft.CmdPal.UI.ViewModels.UnitTests/MainListPageResultFactoryTests.cs

@@ -5,6 +5,7 @@
 using System;
 using System.Collections.Generic;
 using System.Linq;
+using Microsoft.CmdPal.Core.Common.Helpers;
 using Microsoft.CmdPal.UI.ViewModels.Commands;
 using Microsoft.CommandPalette.Extensions;
 using Microsoft.CommandPalette.Extensions.Toolkit;
@@ -43,38 +44,34 @@ public partial class MainListPageResultFactoryTests
         public override string ToString() => Title;
     }
 
-    private static Scored<IListItem> S(string title, int score)
+    private static RoScored<IListItem> S(string title, int score)
     {
-        return new Scored<IListItem>
-        {
-            Score = score,
-            Item = new MockListItem { Title = title },
-        };
+        return new RoScored<IListItem>(score: score, item: new MockListItem { Title = title });
     }
 
     [TestMethod]
     public void Merge_PrioritizesListsCorrectly()
     {
-        var filtered = new List<Scored<IListItem>>
+        var filtered = new List<RoScored<IListItem>>
         {
             S("F1", 100),
             S("F2", 50),
         };
 
-        var scoredFallback = new List<Scored<IListItem>>
+        var scoredFallback = new List<RoScored<IListItem>>
         {
             S("SF1", 100),
             S("SF2", 60),
         };
 
-        var apps = new List<Scored<IListItem>>
+        var apps = new List<RoScored<IListItem>>
         {
             S("A1", 100),
             S("A2", 55),
         };
 
         // Fallbacks are not scored.
-        var fallbacks = new List<Scored<IListItem>>
+        var fallbacks = new List<RoScored<IListItem>>
         {
             S("FB1", 0),
             S("FB2", 0),
@@ -104,7 +101,7 @@ public partial class MainListPageResultFactoryTests
     [TestMethod]
     public void Merge_AppliesAppLimit()
     {
-        var apps = new List<Scored<IListItem>>
+        var apps = new List<RoScored<IListItem>>
         {
             S("A1", 100),
             S("A2", 90),
@@ -126,7 +123,7 @@ public partial class MainListPageResultFactoryTests
     [TestMethod]
     public void Merge_FiltersEmptyFallbacks()
     {
-        var fallbacks = new List<Scored<IListItem>>
+        var fallbacks = new List<RoScored<IListItem>>
         {
             S("FB1", 0),
             S("FB3", 0),

src/modules/cmdpal/Tests/Microsoft.CmdPal.UI.ViewModels.UnitTests/RecentCommandsTests.cs

@@ -5,6 +5,7 @@
 using System;
 using System.Collections.Generic;
 using System.Linq;
+using Microsoft.CmdPal.Core.Common.Text;
 using Microsoft.CmdPal.Ext.UnitTestBase;
 using Microsoft.CmdPal.UI.ViewModels.MainPage;
 using Microsoft.CommandPalette.Extensions;
@@ -263,10 +264,12 @@ public partial class RecentCommandsTests : CommandPaletteUnitTestBase
         };
 
         var history = CreateHistory(items.Reverse<ListItemMock>().ToList());
+        var fuzzyMatcher = CreateMatcher();
+        var q = fuzzyMatcher.PrecomputeQuery("C");
 
-        var scoreA = MainListPage.ScoreTopLevelItem("C", items[0], history);
-        var scoreB = MainListPage.ScoreTopLevelItem("C", items[1], history);
-        var scoreC = MainListPage.ScoreTopLevelItem("C", items[2], history);
+        var scoreA = MainListPage.ScoreTopLevelItem(q, items[0], history, fuzzyMatcher);
+        var scoreB = MainListPage.ScoreTopLevelItem(q, items[1], history, fuzzyMatcher);
+        var scoreC = MainListPage.ScoreTopLevelItem(q, items[2], history, fuzzyMatcher);
 
         // Assert
         // All of these equally match the query, and they're all in the same bucket,
@@ -296,6 +299,11 @@ public partial class RecentCommandsTests : CommandPaletteUnitTestBase
         return history;
     }
 
+    private static IPrecomputedFuzzyMatcher CreateMatcher()
+    {
+        return new PrecomputedFuzzyMatcher(new PrecomputedFuzzyMatcherOptions());
+    }
+
     private sealed record ScoredItem(ListItemMock Item, int Score)
     {
         public string Title => Item.Title;
@@ -337,9 +345,11 @@ public partial class RecentCommandsTests : CommandPaletteUnitTestBase
         var items = CreateMockHistoryItems();
         var emptyHistory = CreateMockHistoryService(new());
         var history = CreateMockHistoryService(items);
+        var fuzzyMatcher = CreateMatcher();
 
-        var unweightedScores = items.Select(item => MainListPage.ScoreTopLevelItem("C", item, emptyHistory)).ToList();
-        var weightedScores = items.Select(item => MainListPage.ScoreTopLevelItem("C", item, history)).ToList();
+        var q = fuzzyMatcher.PrecomputeQuery("C");
+        var unweightedScores = items.Select(item => MainListPage.ScoreTopLevelItem(q, item, emptyHistory, fuzzyMatcher)).ToList();
+        var weightedScores = items.Select(item => MainListPage.ScoreTopLevelItem(q, item, history, fuzzyMatcher)).ToList();
         Assert.AreEqual(unweightedScores.Count, weightedScores.Count, "Both score lists should have the same number of items");
         for (var i = 0; i < unweightedScores.Count; i++)
         {
@@ -380,7 +390,10 @@ public partial class RecentCommandsTests : CommandPaletteUnitTestBase
         var items = CreateMockHistoryItems();
         var emptyHistory = CreateMockHistoryService(new());
         var history = CreateMockHistoryService(items);
-        var weightedScores = items.Select(item => MainListPage.ScoreTopLevelItem("te", item, history)).ToList();
+        var fuzzyMatcher = CreateMatcher();
+        var q = fuzzyMatcher.PrecomputeQuery("te");
+
+        var weightedScores = items.Select(item => MainListPage.ScoreTopLevelItem(q, item, history, fuzzyMatcher)).ToList();
         var weightedMatches = GetMatches(items, weightedScores).ToList();
 
         Assert.AreEqual(3, weightedMatches.Count, "Find Terminal, VsCode and Run commands");
@@ -398,6 +411,8 @@ public partial class RecentCommandsTests : CommandPaletteUnitTestBase
         var items = CreateMockHistoryItems();
         var emptyHistory = CreateMockHistoryService(new());
         var history = CreateMockHistoryService(items);
+        var fuzzyMatcher = CreateMatcher();
+        var q = fuzzyMatcher.PrecomputeQuery("te");
 
         // Add extra uses of VS Code to try and push it above Terminal
         for (var i = 0; i < 10; i++)
@@ -405,7 +420,7 @@ public partial class RecentCommandsTests : CommandPaletteUnitTestBase
             history.AddHistoryItem(items[1].Id);
         }
 
-        var weightedScores = items.Select(item => MainListPage.ScoreTopLevelItem("te", item, history)).ToList();
+        var weightedScores = items.Select(item => MainListPage.ScoreTopLevelItem(q, item, history, fuzzyMatcher)).ToList();
         var weightedMatches = GetMatches(items, weightedScores).ToList();
 
         Assert.AreEqual(3, weightedMatches.Count, "Find Terminal, VsCode and Run commands");
@@ -423,6 +438,8 @@ public partial class RecentCommandsTests : CommandPaletteUnitTestBase
         var items = CreateMockHistoryItems();
         var emptyHistory = CreateMockHistoryService(new());
         var history = CreateMockHistoryService(items);
+        var fuzzyMatcher = CreateMatcher();
+        var q = fuzzyMatcher.PrecomputeQuery("C");
 
         // We're gonna run this test and keep adding more uses of VS Code till
         // it breaks past Command Prompt
@@ -431,7 +448,7 @@ public partial class RecentCommandsTests : CommandPaletteUnitTestBase
         {
             history.AddHistoryItem(vsCodeId);
 
-            var weightedScores = items.Select(item => MainListPage.ScoreTopLevelItem("C", item, history)).ToList();
+            var weightedScores = items.Select(item => MainListPage.ScoreTopLevelItem(q, item, history, fuzzyMatcher)).ToList();
             var weightedMatches = GetMatches(items, weightedScores).ToList();
             Assert.AreEqual(4, weightedMatches.Count);