**Build scan:**
https://gradle-enterprise.elastic.co/s/lxlsgu3jfzm46/tests/:server:test/org.elasticsearch.cluster.coordination.ElectionSchedulerFactoryTests/testRetriesOnCorrectSchedule

**Reproduction line:**
```
gradlew ':server:test' --tests "org.elasticsearch.cluster.coordination.ElectionSchedulerFactoryTests.testRetriesOnCorrectSchedule" -Dtests.seed=9E122BD7EF10E7BD -Dtests.locale=it-IT -Dtests.timezone=Arctic/Longyearbyen -Druntime.java=20
```

**Applicable branches:**
main

**Reproduces locally?:**
Yes

**Failure history:**
https://gradle-enterprise.elastic.co/scans/tests?tests.container=org.elasticsearch.cluster.coordination.ElectionSchedulerFactoryTests&tests.test=testRetriesOnCorrectSchedule

**Failure excerpt:**
```
java.lang.AssertionError: expected to see 1000 retries message but did not
Expected: <true>
     but: was <false>

  at __randomizedtesting.SeedInfo.seed([9E122BD7EF10E7BD:25AEEF51ADC12C72]:0)
  at org.hamcrest.MatcherAssert.assertThat(MatcherAssert.java:18)
  at org.elasticsearch.test.MockLogAppender$SeenEventExpectation.assertMatched(MockLogAppender.java:127)
  at org.elasticsearch.test.MockLogAppender$WrappedLoggingExpectation.assertMatched(MockLogAppender.java:231)
  at org.elasticsearch.test.MockLogAppender.assertAllExpectationsMatched(MockLogAppender.java:61)
  at org.elasticsearch.cluster.coordination.ElectionSchedulerFactoryTests.assertElectionSchedule(ElectionSchedulerFactoryTests.java:127)
  at org.elasticsearch.cluster.coordination.ElectionSchedulerFactoryTests.testRetriesOnCorrectSchedule(ElectionSchedulerFactoryTests.java:179)
  at jdk.internal.reflect.DirectMethodHandleAccessor.invoke(DirectMethodHandleAccessor.java:104)
  at java.lang.reflect.Method.invoke(Method.java:578)
  at com.carrotsearch.randomizedtesting.RandomizedRunner.invoke(RandomizedRunner.java:1758)
  at com.carrotsearch.randomizedtesting.RandomizedRunner$8.evaluate(RandomizedRunner.java:946)
  at com.carrotsearch.randomizedtesting.RandomizedRunner$9.evaluate(RandomizedRunner.java:982)
  at com.carrotsearch.randomizedtesting.RandomizedRunner$10.evaluate(RandomizedRunner.java:996)
  at com.carrotsearch.randomizedtesting.rules.StatementAdapter.evaluate(StatementAdapter.java:36)
  at org.apache.lucene.tests.util.TestRuleSetupTeardownChained$1.evaluate(TestRuleSetupTeardownChained.java:48)
  at org.apache.lucene.tests.util.AbstractBeforeAfterRule$1.evaluate(AbstractBeforeAfterRule.java:43)
  at org.apache.lucene.tests.util.TestRuleThreadAndTestName$1.evaluate(TestRuleThreadAndTestName.java:45)
  at org.apache.lucene.tests.util.TestRuleIgnoreAfterMaxFailures$1.evaluate(TestRuleIgnoreAfterMaxFailures.java:60)
  at org.apache.lucene.tests.util.TestRuleMarkFailure$1.evaluate(TestRuleMarkFailure.java:44)
  at com.carrotsearch.randomizedtesting.rules.StatementAdapter.evaluate(StatementAdapter.java:36)
  at com.carrotsearch.randomizedtesting.ThreadLeakControl$StatementRunner.run(ThreadLeakControl.java:390)
  at com.carrotsearch.randomizedtesting.ThreadLeakControl.forkTimeoutingTask(ThreadLeakControl.java:843)
  at com.carrotsearch.randomizedtesting.ThreadLeakControl$3.evaluate(ThreadLeakControl.java:490)
  at com.carrotsearch.randomizedtesting.RandomizedRunner.runSingleTest(RandomizedRunner.java:955)
  at com.carrotsearch.randomizedtesting.RandomizedRunner$5.evaluate(RandomizedRunner.java:840)
  at com.carrotsearch.randomizedtesting.RandomizedRunner$6.evaluate(RandomizedRunner.java:891)
  at com.carrotsearch.randomizedtesting.RandomizedRunner$7.evaluate(RandomizedRunner.java:902)
  at org.apache.lucene.tests.util.AbstractBeforeAfterRule$1.evaluate(AbstractBeforeAfterRule.java:43)
  at com.carrotsearch.randomizedtesting.rules.StatementAdapter.evaluate(StatementAdapter.java:36)
  at org.apache.lucene.tests.util.TestRuleStoreClassName$1.evaluate(TestRuleStoreClassName.java:38)
  at com.carrotsearch.randomizedtesting.rules.NoShadowingOrOverridesOnMethodsRule$1.evaluate(NoShadowingOrOverridesOnMethodsRule.java:40)
  at com.carrotsearch.randomizedtesting.rules.NoShadowingOrOverridesOnMethodsRule$1.evaluate(NoShadowingOrOverridesOnMethodsRule.java:40)
  at com.carrotsearch.randomizedtesting.rules.StatementAdapter.evaluate(StatementAdapter.java:36)
  at com.carrotsearch.randomizedtesting.rules.StatementAdapter.evaluate(StatementAdapter.java:36)
  at org.apache.lucene.tests.util.TestRuleAssertionsRequired$1.evaluate(TestRuleAssertionsRequired.java:53)
  at org.apache.lucene.tests.util.AbstractBeforeAfterRule$1.evaluate(AbstractBeforeAfterRule.java:43)
  at org.apache.lucene.tests.util.TestRuleMarkFailure$1.evaluate(TestRuleMarkFailure.java:44)
  at org.apache.lucene.tests.util.TestRuleIgnoreAfterMaxFailures$1.evaluate(TestRuleIgnoreAfterMaxFailures.java:60)
  at org.apache.lucene.tests.util.TestRuleIgnoreTestSuites$1.evaluate(TestRuleIgnoreTestSuites.java:47)
  at com.carrotsearch.randomizedtesting.rules.StatementAdapter.evaluate(StatementAdapter.java:36)
  at com.carrotsearch.randomizedtesting.ThreadLeakControl$StatementRunner.run(ThreadLeakControl.java:390)
  at com.carrotsearch.randomizedtesting.ThreadLeakControl.lambda$forkTimeoutingTask$0(ThreadLeakControl.java:850)
  at java.lang.Thread.run(Thread.java:1623)

```
server/src/test/java/org/elasticsearch/cluster/coordination/ElectionSchedulerFactoryTests.java
import static org.hamcrest.Matchers.greaterThanOrEqualTo;
import static org.hamcrest.Matchers.is;
import static org.hamcrest.Matchers.lessThanOrEqualTo;
import static org.hamcrest.Matchers.not;
import static org.hamcrest.Matchers.nullValue;
public class ElectionSchedulerFactoryTests extends ESTestCase {
    private TimeValue randomGracePeriod() {
        return TimeValue.timeValueMillis(randomLongBetween(0, 10000));
    }
    private void assertElectionSchedule(
        final DeterministicTaskQueue deterministicTaskQueue,
        final ElectionSchedulerFactory electionSchedulerFactory,
        final long initialTimeout,
        final long backOffTime,
        final long maxTimeout,
        final long duration
    ) {
        final TimeValue initialGracePeriod = randomGracePeriod();
        final AtomicBoolean electionStarted = new AtomicBoolean();
        final MockLogAppender appender = new MockLogAppender();
        try (
            var ignored0 = appender.capturing(ElectionSchedulerFactory.class);
            var ignored1 = electionSchedulerFactory.startElectionScheduler(
                initialGracePeriod,
                () -> assertTrue(electionStarted.compareAndSet(false, true))
            )
        ) {
            appender.addExpectation(
                new MockLogAppender.UnseenEventExpectation(
                    "no zero retries message",