I don't think that's possible with FileHandler in python.
The workaround is to change the logging FileHandler to StreamHandler, If you have access to pgAdmin4 source code in docker then you can try replacing below line (File: <YOUR_DOCKER_PATH>/pgadmin4/web/pgadmin/__init__.py),
fh = logging.FileHandler(config.LOG_FILE, encoding='utf-8')
with
fh = logging.StreamHandler(sys.stdout)