How to create and register a Logger filter into Spigot/Paper server

build.gradle

//...

dependencies {
  // add Log4j as compileOnly (provided) dependency on your favorite build tool
  compileOnly "org.apache.logging.log4j:log4j-core:2.17.2"
}

MyLogFilter.java

import org.apache.logging.log4j.Level;
import org.apache.logging.log4j.Marker;
import org.apache.logging.log4j.core.Filter;
import org.apache.logging.log4j.core.LogEvent;
import org.apache.logging.log4j.core.Logger;
import org.apache.logging.log4j.core.filter.AbstractFilter;
import org.apache.logging.log4j.message.Message;
import org.jetbrains.annotations.NotNull;
import org.jetbrains.annotations.Nullable;

public class MyLogFilter extends AbstractFilter {

    private static final String STRING_WE_DISLIKE = "Disconnecting com.mojang.authlib.GameProfile@";

    /**
     * This determines if our filter runs <i>before</i> (if {@code true}) or <i>after</i> (if {@code false})
     * the string placeholders are replaced.
     *
     * Usually there's no need to change this.
     */
    private static final boolean USE_RAW_STRING = false;

    public MyLogFilter() {
        // register this filter with the intention of filtering out any message that matches
        // this filter (DENY), else we don't have any particular opinion about it (NEUTRAL)
        //
        // super(onMatch, onMismatch)
        super(Filter.Result.DENY, Filter.Result.NEUTRAL);
    }

    /**
     * Here is where we decide if we want to filter out the message or not. Returning {@link Filter.Result#DENY}
     * (our {@link AbstractFilter#onMatch onMatch}) will filter out the message, and {@link Filter.Result#NEUTRAL}
     * (our {@link AbstractFilter#onMismatch onMismatch}) will leave it alone.
     */
    @NotNull
    private Result doFilter(@Nullable String message) {
        if (message == null || !message.startsWith(STRING_WE_DISLIKE)) {
            return onMismatch;
        }
        return onMatch;
    }

    /**
     * Since this implementation inherits from an abstract filter class, we need to override these four
     * methods to make sure that our filter will be applied to all messages.<br><br>
     *
     * Almost all parameter of all methods below are <b>nullable</b>, you don't need to touch them since
     * we already delegate their results to our important, custom filter method above.
     */
    @Override
    public Result filter(LogEvent event) {
        Message msg = event == null ? null : event.getMessage();
        String message = msg == null ? null : (USE_RAW_STRING 
                ? msg.getFormat()
                : msg.getFormattedMessage());
        return doFilter(message);
    }

    @Override
    public Result filter(Logger logger, Level level, Marker marker, Object msg, Throwable t) {
        return doFilter(msg == null ? null : msg.toString());
    }

    @Override
    public Result filter(Logger logger, Level level, Marker marker, String msg, Object... params) {
        return doFilter(msg);
    }

    @Override
    public Result filter(Logger logger, Level level, Marker marker, Message msg, Throwable t) {
        String message = msg == null ? null : (USE_RAW_STRING
                ? msg.getFormat()
                : msg.getFormattedMessage());
        return doFilter(message);
    }
}

MyMainClass.java

import yourpkg.yourplugin.filter.MyLogFilter;
import org.apache.logging.log4j.LogManager;
import org.apache.logging.log4j.core.Filter;
import org.apache.logging.log4j.core.Logger;
import org.bukkit.plugin.java.JavaPlugin;

public class MyMainClass extends JavaPlugin  {

    @Override
    public void onEnable() {
        // do your things, then register the filters
        registerLoggerFilters(new MyLogFilter());
    }

    private void registerLoggerFilters(Filter... filters) {
        org.apache.logging.log4j.Logger rootLogger = LogManager.getRootLogger();
        if (!(rootLogger instanceof Logger)) {
            // in case the root logger is not the expected instance of Logger, just return
            // because there is something wrong
            return;
        }

        Logger logger = (Logger) rootLogger;
        for (Filter filter : filters) {
            // register all filters onto the root logger
            logger.addFilter(filter);
        }
    }
}

pom.xml

//...

<!-- add Log4j as provided (compileOnly) dependency on your favorite build tool -->
<dependency>
    <groupId>org.apache.logging.log4j</groupId>
    <artifactId>log4j-core</artifactId>
    <version>2.17.2</version>
    <scope>provided</scope>
</dependency>