Run AOT-published binary after publishing to verify it succeeds

Co-authored-by: stephentoub <2642209+stephentoub@users.noreply.github.com>

Author: Copilot

Makefile

@@ -31,7 +31,8 @@ test: build
 		RunConfiguration.CollectSourceInformation=true
 
 test-aot:
-	dotnet publish tests/ModelContextProtocol.AotCompatibility.TestApp/ModelContextProtocol.AotCompatibility.TestApp.csproj --configuration $(CONFIGURATION)
+	dotnet publish tests/ModelContextProtocol.AotCompatibility.TestApp/ModelContextProtocol.AotCompatibility.TestApp.csproj --configuration $(CONFIGURATION) -o $(ARTIFACT_PATH)/aot-publish
+	$(ARTIFACT_PATH)/aot-publish/ModelContextProtocol.AotCompatibility.TestApp
 
 pack: restore
 	dotnet pack --no-restore --configuration $(CONFIGURATION)