This looks to be a newly added test in #89430 and failed for me in a PR.

**Build scan:**
https://gradle-enterprise.elastic.co/s/ctyyqap6ywxok/tests/:server:test/org.elasticsearch.index.shard.IndexShardTests/testFlushOnIdleConcurrentFlushDoesNotWait

**Reproduction line:**
`./gradlew ':server:test' --tests "org.elasticsearch.index.shard.IndexShardTests.testFlushOnIdleConcurrentFlushDoesNotWait" -Dtests.seed=3B825C4D0772201A -Dtests.locale=ru-RU -Dtests.timezone=Australia/Broken_Hill -Druntime.java=17`

**Applicable branches:**
main

**Reproduces locally?:**
No

**Failure history:**
https://gradle-enterprise.elastic.co/scans/tests?tests.container=org.elasticsearch.index.shard.IndexShardTests&tests.test=testFlushOnIdleConcurrentFlushDoesNotWait

**Failure excerpt:**
```
java.lang.AssertionError: expected to see should see first flush getting lock immediately but did not
Expected: <true>
     but: was <false>

  at __randomizedtesting.SeedInfo.seed([3B825C4D0772201A:B93D2E3091554306]:0)
  at org.hamcrest.MatcherAssert.assertThat(MatcherAssert.java:18)
  at org.elasticsearch.test.MockLogAppender$SeenEventExpectation.assertMatched(MockLogAppender.java:121)
  at org.elasticsearch.test.MockLogAppender.assertAllExpectationsMatched(MockLogAppender.java:55)
  at org.elasticsearch.test.ESTestCase.assertBusy(ESTestCase.java:1104)
  at org.elasticsearch.test.ESTestCase.assertBusy(ESTestCase.java:1077)
  at org.elasticsearch.index.shard.IndexShardTests.testFlushOnIdleConcurrentFlushDoesNotWait(IndexShardTests.java:3939)
  at jdk.internal.reflect.NativeMethodAccessorImpl.invoke0(NativeMethodAccessorImpl.java:-2)
  at jdk.internal.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:77)
  at jdk.internal.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)
  at java.lang.reflect.Method.invoke(Method.java:568)
  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:44)
  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:833)

```
server/src/test/java/org/elasticsearch/index/shard/IndexShardTests.java
config.getAnalyzer(),
                config.getSimilarity(),
                new CodecService(null, BigArrays.NON_RECYCLING_INSTANCE),
                config.getEventListener(),
                config.getQueryCache(),
                config.getQueryCachingPolicy(),
                config.getTranslogConfig(),
                config.getFlushMergesAfter(),
                config.getExternalRefreshListener(),
                config.getInternalRefreshListener(),
                config.getIndexSort(),
                config.getCircuitBreakerService(),
                config.getGlobalCheckpointSupplier(),
                config.retentionLeasesSupplier(),
                config.getPrimaryTermSupplier(),
                IndexModule.DEFAULT_SNAPSHOT_COMMIT_SUPPLIER,
                config.getLeafSorter()
            );
            return new InternalEngine(configWithWarmer);
        });
        Thread recoveryThread = new Thread(() -> expectThrows(AlreadyClosedException.class, () -> recoverShardFromStore(shard)));
        recoveryThread.start();
        try {
            warmerStarted.await();
            shard.close("testing", false);
            assertThat(shard.state, equalTo(IndexShardState.CLOSED));
        } finally {
            warmerBlocking.countDown();
        }
        recoveryThread.join();