[CmdPal][UT] Refactor some cmdpal ext's ut and improve the test case (#40896)

<!-- Enter a brief description/summary of your PR here. What does it
fix/what does it change/how was it tested (even manually, if necessary)?
-->
## Summary of the Pull Request
1. Remove some AI generated nonsense case
2. Add ISettingsInterface for those ext for testing purpose.
3. Add query test.

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

- [x] Closes: #40897
- [x] **Communication:** I've discussed this with core contributors
already. If the work hasn't been agreed, this work might be rejected
- [x] **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

---------

Co-authored-by: Yu Leng <yuleng@microsoft.com>

src/modules/cmdpal/Tests/Microsoft.CmdPal.Ext.Registry.UnitTests/Microsoft.CmdPal.Ext.Registry.UnitTests.csproj

@@ -18,5 +18,6 @@
 
   <ItemGroup>
     <ProjectReference Include="..\..\ext\Microsoft.CmdPal.Ext.Registry\Microsoft.CmdPal.Ext.Registry.csproj" />
+    <ProjectReference Include="..\Microsoft.CmdPal.Ext.UnitTestsBase\Microsoft.CmdPal.Ext.UnitTestBase.csproj" />
   </ItemGroup>
 </Project>

src/modules/cmdpal/Tests/Microsoft.CmdPal.Ext.Registry.UnitTests/QueryTests.cs

@@ -0,0 +1,74 @@
+// 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.Linq;
+using Microsoft.CmdPal.Ext.Registry.Helpers;
+using Microsoft.CmdPal.Ext.UnitTestBase;
+using Microsoft.CommandPalette.Extensions;
+using Microsoft.CommandPalette.Extensions.Toolkit;
+using Microsoft.VisualStudio.TestTools.UnitTesting;
+
+namespace Microsoft.CmdPal.Ext.Registry.UnitTests;
+
+[TestClass]
+public class QueryTests : CommandPaletteUnitTestBase
+{
+    [DataTestMethod]
+    [DataRow("HKLM", "HKEY_LOCAL_MACHINE")]
+    [DataRow("HKCU", "HKEY_CURRENT_USER")]
+    [DataRow("HKCR", "HKEY_CLASSES_ROOT")]
+    [DataRow("HKU", "HKEY_USERS")]
+    [DataRow("HKCC", "HKEY_CURRENT_CONFIG")]
+    public void TopLevelPageQueryTest(string input, string expectedKeyName)
+    {
+        var settings = new Settings();
+        var page = new RegistryListPage(settings);
+        var results = page.Query(input);
+
+        Assert.IsNotNull(results);
+        Assert.IsTrue(results.Count > 0, "No items matched the query.");
+
+        var firstItem = results.FirstOrDefault();
+        Assert.IsNotNull(firstItem, "No items matched the query.");
+        Assert.IsTrue(
+            firstItem.Title.Contains(expectedKeyName, System.StringComparison.OrdinalIgnoreCase),
+            $"Expected to match '{expectedKeyName}' but got '{firstItem.Title}'");
+    }
+
+    [TestMethod]
+    public void EmptyQueryTest()
+    {
+        var settings = new Settings();
+        var page = new RegistryListPage(settings);
+        var results = page.Query(string.Empty);
+
+        Assert.IsNotNull(results);
+
+        // Empty query should return all base keys
+        Assert.IsTrue(results.Count >= 5, "Expected at least 5 base registry keys.");
+    }
+
+    [TestMethod]
+    public void NullQueryTest()
+    {
+        var settings = new Settings();
+        var page = new RegistryListPage(settings);
+        var results = page.Query(null);
+
+        Assert.IsNotNull(results);
+        Assert.AreEqual(0, results.Count, "Null query should return empty results.");
+    }
+
+    [TestMethod]
+    public void InvalidBaseKeyTest()
+    {
+        var settings = new Settings();
+        var page = new RegistryListPage(settings);
+        var results = page.Query("INVALID_KEY");
+
+        Assert.IsNotNull(results);
+
+        Assert.AreEqual(0, results.Count, "Invalid query should return empty results.");
+    }
+}

src/modules/cmdpal/Tests/Microsoft.CmdPal.Ext.Registry.UnitTests/Settings.cs

@@ -0,0 +1,15 @@
+// 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 Microsoft.CmdPal.Ext.Registry.Helpers;
+
+namespace Microsoft.CmdPal.Ext.Registry.UnitTests;
+
+public class Settings : ISettingsInterface
+{
+    public Settings()
+    {
+        // Currently no specific settings for Registry extension
+    }
+}