Refine the CmdPal launch and activation logic when opening a new app instance

[lei9444]

Summary of the Pull Request

This PR address https://github.com/microsoft/PowerToys/issues/39376

Key changes:

1. Ensures RedirectActivationToAsync(args) is properly awaited using .GetAwaiter().GetResult() to preserve activation data.
2. Uses DispatcherQueue.TryEnqueue to safely handle UI thread execution and avoid COMException during window activation.
3. Addresses a race condition in Logger.InitializeLogger where multiple instances could trigger creation of unexpected log files. The root cause is that TextWriterTraceListener attempts to create a log file even if the target file is already in use, which results in a fallback file path prefixed with a GUID.

PR Checklist

• [x] Closes: #39376
• [ ] Communication: I've discussed this with core contributors already. If 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 for new binaries
  • [ ] WXS for installer for new binaries and localization folder
  • [ ] YML for CI pipeline for new test projects
  • [ ] YML for signed pipeline
• [ ] Documentation updated: If checked, please file a pull request on our docs repo and link it here: #xxx

Detailed Description of the Pull Request / Additional comments

Validation Steps Performed