Settings: Settings search fixes (#41381)

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fix/what does it change/how was it tested (even manually, if necessary)?
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## Summary of the Pull Request
Fix 3 issues

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## PR Checklist

- [x] Closes: #41369, #41374, #41380
- [ ] **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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## Detailed Description of the Pull Request / Additional comments

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https://github.com/user-attachments/assets/0e0df9fb-5aca-4b26-9d53-e6ddc49cab04

---------

Co-authored-by: Niels Laute <niels.laute@live.nl>
Co-authored-by: Jiří Polášek <me@jiripolasek.com>

src/settings-ui/Settings.UI/PowerToys.Settings.csproj

@@ -181,9 +181,6 @@
 		</Page>
 	</ItemGroup>
 
-	<!-- Removed nested publish/exec and copy targets. -->
-
-	<!-- Build XamlIndexBuilder before compiling Settings to ensure the search index exists without taking a project reference. -->
 	<Target Name="BuildXamlIndexBeforeSettings" BeforeTargets="CoreCompile">
 		<Message Importance="high" Text="[Settings] Building XamlIndexBuilder prior to compile. Views='$(MSBuildProjectDirectory)\SettingsXAML\Views' Out='$(GeneratedJsonFile)'" />
 		<MSBuild Projects="..\Settings.UI.XamlIndexBuilder\Settings.UI.XamlIndexBuilder.csproj" Targets="Build" Properties="Configuration=$(Configuration);Platform=Any CPU;TargetFramework=net9.0;XamlViewsDir=$(MSBuildProjectDirectory)\SettingsXAML\Views;GeneratedJsonFile=$(GeneratedJsonFile)" />