CmdPal: Improve error handling and logging in activation process (#41344)

## Summary of the Pull Request

This PR makes passing arguments from a new instance to the existing one
more resilient:


- Fixes situations where `x-cmdpal://` links might not work as expected.
Instead of performing the intended action (e.g., `x-cmdpal://background`
or `x-cmdpal://settings`), they could incorrectly just summon the main
window.

- Refactors the `AppInstance.Activated` handler to be synchronous.  
- The handler blocks `AppInstance.RedirectActivationToAsync` in the
caller.
- If it runs asynchronously (or offloads work to another thread,
including the UI thread), the calling instance may exit too soon,
preventing the activation arguments from being read.

- Adds a timeout and ensures the semaphore is always released so the
application can exit gracefully under all conditions.

- Adjusts handling for cases where the source application exits before
passing arguments by lowering the log severity to **Warning** and
providing a clearer, more descriptive message.

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## PR Checklist

- [ ] Closes: #xxx
- [ ] **Communication:** I've discussed this with core contributors
already. If the work hasn't been agreed, this work might be rejected
- [x] **Tests:** yop
- [x] **Localization:** no need
- [x] **Dev docs:** no need
- [x] **New binaries:** none
- [x] **Documentation updated:** nope

<!-- 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
Tested with x-cmdpal://settings under normal conditions, and with CmdPal
deliberately slowed down to take its sweet time handling the arguments
(so the calling instance times out).

src/modules/cmdpal/Microsoft.CmdPal.UI/App.xaml.cs

@@ -85,7 +85,7 @@ public partial class App : Application
         AppWindow = new MainWindow();
 
         var activatedEventArgs = Microsoft.Windows.AppLifecycle.AppInstance.GetCurrent().GetActivatedEventArgs();
-        ((MainWindow)AppWindow).HandleLaunch(activatedEventArgs);
+        ((MainWindow)AppWindow).HandleLaunchNonUI(activatedEventArgs);
     }
 
     /// <summary>