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.

<!-- Please review the items on the PR checklist before submitting-->
## 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/Program.cs

@@ -107,12 +107,33 @@ internal sealed class Program
     {
         // Do the redirection on another thread, and use a non-blocking
         // wait method to wait for the redirection to complete.
-        var redirectSemaphore = new Semaphore(0, 1);
-        Task.Run(() =>
+        using var redirectSemaphore = new Semaphore(0, 1);
+        var redirectTimeout = TimeSpan.FromSeconds(32);
+
+        _ = Task.Run(() =>
         {
-            keyInstance.RedirectActivationToAsync(args).AsTask().Wait();
-            redirectSemaphore.Release();
+            using var cts = new CancellationTokenSource(redirectTimeout);
+            try
+            {
+                keyInstance.RedirectActivationToAsync(args)
+                    .AsTask(cts.Token)
+                    .GetAwaiter()
+                    .GetResult();
+            }
+            catch (OperationCanceledException)
+            {
+                Logger.LogError($"Failed to activate existing instance; timed out after {redirectTimeout}.");
+            }
+            catch (Exception ex)
+            {
+                Logger.LogError("Failed to activate existing instance", ex);
+            }
+            finally
+            {
+                redirectSemaphore.Release();
+            }
         });
+
         _ = PInvoke.CoWaitForMultipleObjects(
             (uint)CWMO_FLAGS.CWMO_DEFAULT,
             PInvoke.INFINITE,
@@ -124,13 +145,14 @@ internal sealed class Program
     {
         // If we already have a form, display the message now.
         // Otherwise, add it to the collection for displaying later.
-        if (App.Current is App thisApp)
+        if (App.Current?.AppWindow is MainWindow mainWindow)
         {
-            if (thisApp.AppWindow is not null and
-                MainWindow mainWindow)
-            {
-                uiContext?.Post(_ => mainWindow.HandleLaunch(args), null);
-            }
+            // LOAD BEARING
+            // This must be synchronous to ensure the method does not return
+            // before the activation is fully handled and the parameters are processed.
+            // The sending instance remains blocked until this returns; afterward it may quit,
+            // causing the activation arguments to be lost.
+            mainWindow.HandleLaunchNonUI(args);
         }
     }
 }