The problem is that the other code most likely uses a different logger. With java.util.logging you can configure the root-logger right when the application starts and the other loggers will inherit the configuration.

private static void configureRootLogger() {
    try {
        FileHandler fh = new FileHandler("MyLogFile.log");
        fh.setFormatter(new SimpleFormatter());
        Logger.getLogger("").addHandler(fh);
    } catch (IOException e) {
        // handle exception
    }
}

Full example:

import java.io.IOException;
import java.util.logging.FileHandler;
import java.util.logging.Logger;
import java.util.logging.SimpleFormatter;

public class LogToFileExample {

    private static final Logger logger = Logger.getLogger("MyLogA");

    public static void main(String[] args) {
        configureRootLogger();
        logger.info("local test message");
        final LogTester tester = new LogTester();
        tester.logMessage();
    }

    private static void configureRootLogger() {
        try {
            FileHandler fh = new FileHandler("MyLogFile.log");
            fh.setFormatter(new SimpleFormatter());
            Logger.getLogger("").addHandler(fh);
        } catch (IOException e) {
            logger.warning("Could not add handler to log to file");
        }
    }
}

import java.util.logging.Logger;

public class LogTester {

    private static final Logger logger = Logger.getLogger("MyLogB");

    public void logMessage() {
        logger.info("external log message");
    }
}

Identical output in file and console:

May 28, 2021 9:44:50 AM org.testing.LogToFileExample main
INFO: local test message
May 28, 2021 9:44:50 AM org.testing.LogTester logMessage
INFO: external log message

See this short introduction to log4j.

The issue is in using System.out to print debugging or diagnostic information. It is a bad practice because you cannot easily change log levels, turn it off, customize it, etc.

However if you are legitimately using System.out to print information to the user, then you can ignore this warning.

I believe the default logging level is Level.ERROR, which means that only calls to log.error() (and nothing else) will result in log information being recorded. You need to configure the log level you actually want, e.g. by adding this:

appender.setThreshold(Level.INFO);

This means your logger will output every message from INFO priority and above. Of course you could put a lower level such as Level.DEBUG.

EDIT

On the other hand, your log is not static, but is is used from static methods, so you need to change it.