Handle exception thrown by ProcessName during ProcessEx timeout (#23990)

* Handle exception thrown by ProcessName during ProcessEx timeout

* Update src/Shared/Process/ProcessEx.cs

Co-authored-by: Brennan <brecon@microsoft.com>

* PR feedback

Co-authored-by: Brennan <brecon@microsoft.com>

src/Shared/Process/ProcessEx.cs

@@ -49,10 +49,15 @@ namespace Microsoft.AspNetCore.Internal
 
             _exited = new TaskCompletionSource<int>(TaskCreationOptions.RunContinuationsAsynchronously);
 
+            // We greedily create a timeout exception message even though a timeout is unlikely to happen for two reasons:
+            // 1. To make it less likely for Process getters to throw exceptions like "System.InvalidOperationException: Process has exited, ..."
+            // 2. To ensure if/when exceptions are thrown from Process getters, these exceptions can easily be observed.
+            var timeoutExMessage = $"Process proc {proc.ProcessName} {proc.StartInfo.Arguments} timed out after {DefaultProcessTimeout}.";
+
             _processTimeoutCts = new CancellationTokenSource(timeout);
             _processTimeoutCts.Token.Register(() =>
             {
-                _exited.TrySetException(new TimeoutException($"Process proc {proc.ProcessName} {proc.StartInfo.Arguments} timed out after {DefaultProcessTimeout}."));
+                _exited.TrySetException(new TimeoutException(timeoutExMessage));
             });
         }