IGNITE-17717 Fix APP_ID for Log4j2Logger (#10275)

(cherry picked from commit e6733bad6e319126bf40dfbd8f15fcce332af2a1)
diff --git a/modules/log4j2/src/main/java/org/apache/ignite/logger/log4j2/Log4J2Logger.java b/modules/log4j2/src/main/java/org/apache/ignite/logger/log4j2/Log4J2Logger.java
index 2dde4fd..73ec276 100644
--- a/modules/log4j2/src/main/java/org/apache/ignite/logger/log4j2/Log4J2Logger.java
+++ b/modules/log4j2/src/main/java/org/apache/ignite/logger/log4j2/Log4J2Logger.java
@@ -238,6 +238,8 @@
      */
     static void cleanup() {
         synchronized (mux) {
+            System.clearProperty(APP_ID);
+
             if (inited)
                 LogManager.shutdown();
 
@@ -424,7 +426,9 @@
 
         // Set nodeId as system variable to be used at configuration.
         System.setProperty(NODE_ID, U.id8(nodeId));
-        System.setProperty(APP_ID, application != null ? application : "ignite");
+        System.setProperty(APP_ID, application != null
+            ? application
+            : System.getProperty(APP_ID, "ignite"));
 
         if (inited) {
             synchronized (mux) {
diff --git a/modules/log4j2/src/test/java/org/apache/ignite/logger/log4j2/Log4j2LoggerSelfTest.java b/modules/log4j2/src/test/java/org/apache/ignite/logger/log4j2/Log4j2LoggerSelfTest.java
index 6c2571c..04fe17e 100644
--- a/modules/log4j2/src/test/java/org/apache/ignite/logger/log4j2/Log4j2LoggerSelfTest.java
+++ b/modules/log4j2/src/test/java/org/apache/ignite/logger/log4j2/Log4j2LoggerSelfTest.java
@@ -146,6 +146,11 @@
 
         assertEquals(U.id8(id), System.getProperty("nodeId"));
         assertEquals("other-app", System.getProperty("appId"));
+
+        new Log4J2Logger(LOG_PATH_TEST).setApplicationAndNode(null, id);
+
+        assertEquals(U.id8(id), System.getProperty("nodeId"));
+        assertEquals("other-app", System.getProperty("appId"));
     }
 
     /**