CmdPal: Keep TimeDateExtensionPage simple and update every time (#46396)

## Summary of the Pull Request

This PR updates Time & Date extension page to calculate current results
every time. This breaks possible infinite loop.

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## PR Checklist

- [x] Closes: #46329
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issues) -->
- [ ] **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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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.Ext.TimeDate.UnitTests/QueryTests.cs

@@ -68,7 +68,7 @@ public class QueryTests : CommandPaletteUnitTestBase
     {
         var settings = new Settings();
         var page = new TimeDateExtensionPage(settings);
-        page.UpdateSearchText(string.Empty, input);
+        page.SearchText = input;
         var resultLists = page.GetItems();
 
         var result = Query(input, resultLists);
@@ -117,7 +117,7 @@ public class QueryTests : CommandPaletteUnitTestBase
     {
         var settings = new Settings();
         var page = new TimeDateExtensionPage(settings);
-        page.UpdateSearchText(string.Empty, input);
+        page.SearchText = input;
         var resultLists = page.GetItems();
 
         var firstItem = resultLists.FirstOrDefault();
@@ -158,7 +158,7 @@ public class QueryTests : CommandPaletteUnitTestBase
     {
         var settings = new Settings();
         var page = new TimeDateExtensionPage(settings);
-        page.UpdateSearchText(string.Empty, query);
+        page.SearchText = query;
         var results = page.GetItems();
 
         // Assert
@@ -176,7 +176,8 @@ public class QueryTests : CommandPaletteUnitTestBase
     {
         var settings = new Settings();
         var page = new TimeDateExtensionPage(settings);
-        page.UpdateSearchText("abc", input);
+        page.SearchText = "abc";
+        page.SearchText = input;
         var results = page.GetItems();
 
         // Assert
@@ -193,7 +194,7 @@ public class QueryTests : CommandPaletteUnitTestBase
     {
         var settings = new Settings();
         var page = new TimeDateExtensionPage(settings);
-        page.UpdateSearchText(string.Empty, query);
+        page.SearchText = query;
         var resultsList = page.GetItems();
         var results = Query(query, resultsList);
 
@@ -211,7 +212,7 @@ public class QueryTests : CommandPaletteUnitTestBase
     {
         var settings = new Settings();
         var page = new TimeDateExtensionPage(settings);
-        page.UpdateSearchText(string.Empty, query);
+        page.SearchText = query;
         var resultsList = page.GetItems();
 
         // Assert
@@ -219,4 +220,28 @@ public class QueryTests : CommandPaletteUnitTestBase
         var firstResult = resultsList.FirstOrDefault();
         Assert.IsTrue(firstResult.Title.Contains(expectedResult, StringComparison.CurrentCulture), $"Delimiter query '{query}' result not match {expectedResult} current result {firstResult.Title}");
     }
+
+    [TestMethod]
+    public void UpdateSearchTextMatchesSearchTextSetter()
+    {
+        var settings = new Settings();
+        var pageUsingSetter = new TimeDateExtensionPage(settings);
+        var pageUsingMethod = new TimeDateExtensionPage(settings);
+        const string query = "time::12:30:45";
+
+        pageUsingSetter.SearchText = query;
+        pageUsingMethod.UpdateSearchText(string.Empty, query);
+
+        var setterResults = pageUsingSetter.GetItems();
+        var methodResults = pageUsingMethod.GetItems();
+
+        Assert.AreEqual(setterResults.Length, methodResults.Length, "UpdateSearchText should produce the same number of results as setting SearchText.");
+
+        var setterFirstItem = setterResults.FirstOrDefault();
+        var methodFirstItem = methodResults.FirstOrDefault();
+        Assert.IsNotNull(setterFirstItem);
+        Assert.IsNotNull(methodFirstItem);
+        Assert.AreEqual(setterFirstItem.Title, methodFirstItem.Title, "UpdateSearchText should keep the stored query in sync with SearchText.");
+        Assert.AreEqual(setterFirstItem.Subtitle, methodFirstItem.Subtitle, "UpdateSearchText should keep the stored query in sync with SearchText.");
+    }
 }