Refactor watcher_test into integration_tests. (#4220)

Author: davidmorgan

build_runner/pubspec.yaml

@@ -53,7 +53,6 @@ dev_dependencies:
   stream_channel: ^2.0.0
   test: ^1.25.5
   test_descriptor: ^2.0.0
-  test_process: ^2.0.0
 
 topics:
  - build-runner