[CI] FileSettingsServiceIT testErrorCanRecoverOnRestart failing (#116895) (#117511) (#117558)

Fixes flaky test FileSettingsServiceIT.testErrorCanRecoverOnRestart
Fixes #116895

server/src/internalClusterTest/java/org/elasticsearch/reservedstate/service/FileSettingsServiceIT.java

@@ -398,7 +398,7 @@ public class FileSettingsServiceIT extends ESIntegTestCase {
 
         FileSettingsService masterFileSettingsService = internalCluster().getInstance(FileSettingsService.class, masterNode);
 
-        assertTrue(masterFileSettingsService.watching());
+        assertBusy(() -> assertTrue(masterFileSettingsService.watching()));
         assertFalse(dataFileSettingsService.watching());
 
         writeJSONFile(masterNode, testErrorJSON, logger, versionCounter.incrementAndGet());
@@ -434,7 +434,7 @@ public class FileSettingsServiceIT extends ESIntegTestCase {
 
         FileSettingsService masterFileSettingsService = internalCluster().getInstance(FileSettingsService.class, masterNode);
 
-        assertTrue(masterFileSettingsService.watching());
+        assertBusy(() -> assertTrue(masterFileSettingsService.watching()));
         assertFalse(dataFileSettingsService.watching());
 
         writeJSONFile(masterNode, testErrorJSON, logger, versionCounter.incrementAndGet());