add initial solution (made with copilot)

src/Core/LoggerFactory.php

@@ -0,0 +1,19 @@
+<?php
+namespace Core;
+
+use Monolog\Logger;
+use Monolog\Handler\SyslogHandler;
+use Monolog\Processor\UidProcessor;
+use Monolog\Formatter\JsonFormatter;
+
+class LoggerFactory {
+    public static function create(string $name = null): Logger {
+        $ident = $name ?? Config::get('log_ident', 'api');
+        $logger = new Logger($ident);
+        $handler = new SyslogHandler($ident, LOG_USER);
+        $handler->setFormatter(new JsonFormatter());
+        $logger->pushHandler($handler);
+        $logger->pushProcessor(new UidProcessor());
+        return $logger;
+    }
+}