## 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
<!-- Please review the items on the PR checklist before submitting-->
## 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
<!-- 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
_targets #40504_
Major refactoring for #40113
This moves a large swath of the codebase to a `.Core` project. "Core"
doesn't have any explicit dependencies on "extensions", settings or the
current `MainListPage`. It's just a filterable list of stuff. This
should let us make this component a bit more reusable.
This is half of a PR. As I did this, I noticed a particular bit of code
for TopLevelVViewModels and CommandPaletteHost that was _very rough_.
Solving it in this PR would make "move everything to a new project" much
harder to review. So I'm submitting two PRs simultaneously, so we can
see the changes separately, then merge together.
