I'm logging errors too. LoggingContextFilter.

This makes it easy to see errors in background processes when you're
writing unit tests. Otherwise, you have to know/remember to look at the
test logs in `_trial_temp`.

changelog.d/10657.misc

@@ -0,0 +1 @@
+Log errors in tests to stderr.

tests/test_utils/logging_setup.py

@@ -13,6 +13,7 @@
 # limitations under the License.
 import logging
 import os
+import sys
 
 import twisted.logger
 
@@ -35,7 +36,8 @@ class ToTwistedHandler(logging.Handler):
 def setup_logging():
     """Configure the python logging appropriately for the tests.
 
-    (Logs will end up in _trial_temp.)
+    Logs will end up in _trial_temp. Errors are additionally
+    logged to stderr.
     """
     root_logger = logging.getLogger()
 
@@ -43,12 +45,19 @@ def setup_logging():
         "%(asctime)s - %(name)s - %(lineno)d - "
         "%(levelname)s - %(request)s - %(message)s"
     )
-
-    handler = ToTwistedHandler()
     formatter = logging.Formatter(log_format)
-    handler.setFormatter(formatter)
-    handler.addFilter(LoggingContextFilter())
-    root_logger.addHandler(handler)
+    filter = LoggingContextFilter()
+
+    to_twisted_handler = ToTwistedHandler()
+    to_twisted_handler.setFormatter(formatter)
+    to_twisted_handler.addFilter(filter)
+    root_logger.addHandler(to_twisted_handler)
+
+    error_handler = logging.StreamHandler(sys.stderr)
+    error_handler.setLevel(logging.ERROR)
+    error_handler.setFormatter(formatter)
+    error_handler.addFilter(filter)
+    root_logger.addHandler(error_handler)
 
     log_level = os.environ.get("SYNAPSE_TEST_LOG_LEVEL", "ERROR")
     root_logger.setLevel(log_level)