Fix for structured logging tests stomping on logs (#6023)

MANIFEST.in

changelog.d/6023.misc

mypy.ini

synapse/config/logger.py

synapse/logging/_structured.py

synapse/logging/_terse_json.py

synapse/logging/opentracing.py

synapse/metrics/__init__.py

synapse/metrics/_exposition.py

synapse/python_dependencies.py

tests/logging/test_structured.py

tests/logging/test_terse_json.py

tox.ini