[Linux] Add a 'flutter run' console output test (#118279)

* Add Linux support for the UI integration test project

* Add Linux run console test
diff --git a/TESTOWNERS b/TESTOWNERS
index b6ca461..c2b41f3 100644
--- a/TESTOWNERS
+++ b/TESTOWNERS
@@ -251,8 +251,10 @@
 /dev/devicelab/bin/tasks/plugin_test_macos.dart @jmagman @flutter/desktop
 /dev/devicelab/bin/tasks/plugin_test.dart @stuartmorgan @flutter/plugin
 /dev/devicelab/bin/tasks/run_debug_test_android.dart @zanderso @flutter/tool
+/dev/devicelab/bin/tasks/run_debug_test_linux.dart @loic-sharma @flutter/tool
 /dev/devicelab/bin/tasks/run_debug_test_macos.dart @cbracken @flutter/tool
 /dev/devicelab/bin/tasks/run_debug_test_windows.dart @loic-sharma @flutter/tool
+/dev/devicelab/bin/tasks/run_release_test_linux.dart @loic-sharma @flutter/tool
 /dev/devicelab/bin/tasks/run_release_test_macos.dart @cbracken @flutter/tool
 /dev/devicelab/bin/tasks/run_release_test_windows.dart @loic-sharma @flutter/tool
 /dev/devicelab/bin/tasks/technical_debt__cost.dart @HansMuller @flutter/framework