CmdPal: Fix Dock context menu following active item in Command Bar (#46420)

## Summary of the Pull Request

This PR decouples the Dock control context menu from the item selected
in the Shell Page list / Command Bar.

- Adds a new property to the context menu to control whether it should
react to messages like `UpdateCommandBarMessage`
- The `DockControl` context menu no longer follows those messages

Additional changes:

- Ensures the context menu for Dock-selected search box position
reflects the Dock position (when the Dock is at the bottom, the search
box is also at the bottom)
- Consistently displays the dock item context menu even for items with a
single context menu action (instead of showing the Dock menu, which was
confusing)

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## PR Checklist

- [x] Closes: #46404
- [x] Closes: #45892
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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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## Detailed Description of the Pull Request / Additional comments

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