CmdPal: Bind FilterDropDown selection to the current filter and ensure notifications are raised on UI thread (#41808)

## Summary of the Pull Request

This PR declaratively binds FilterDropDown.SelectedValue to
CurrentFilterId (one-way only; updates in the opposite direction are
handled within the drop-down’s code). It also removes observable
properties and reverts to the UpdateProperty style to ensure property
change notifications are raised on the UI thread, aligning the handling
style with other classes.

## Impact
- Fixed a crash that could occur on pages with filters
- The filter drop-down now correctly syncs with the initially selected
filter when loading a page

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## PR Checklist

- [x] Closes: #41578
- [x] Closes: #41649
- [ ] **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

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## Validation Steps Performed

src/modules/cmdpal/Microsoft.CmdPal.Core.ViewModels/ExtensionObjectViewModel.cs

@@ -51,6 +51,36 @@ public abstract partial class ExtensionObjectViewModel : ObservableObject
         DoOnUiThread(() => OnPropertyChanged(propertyName));
     }
 
+    protected void UpdateProperty(string propertyName1, string propertyName2)
+    {
+        DoOnUiThread(() =>
+        {
+            OnPropertyChanged(propertyName1);
+            OnPropertyChanged(propertyName2);
+        });
+    }
+
+    protected void UpdateProperty(string propertyName1, string propertyName2, string propertyName3)
+    {
+        DoOnUiThread(() =>
+        {
+            OnPropertyChanged(propertyName1);
+            OnPropertyChanged(propertyName2);
+            OnPropertyChanged(propertyName3);
+        });
+    }
+
+    protected void UpdateProperty(params string[] propertyNames)
+    {
+        DoOnUiThread(() =>
+        {
+            foreach (var propertyName in propertyNames)
+            {
+                OnPropertyChanged(propertyName);
+            }
+        });
+    }
+
     protected void ShowException(Exception ex, string? extensionHint = null)
     {
         if (PageContext.TryGetTarget(out var pageContext))