Although it's an ML test suite, the problems all look to be because an index was deleted while a recovery was ongoing and but the recovery task never goes away.

**Build scan:**
https://gradle-enterprise.elastic.co/s/e3zjigozbae3y/tests/:x-pack:plugin:ml:qa:native-multi-node-tests:javaRestTest/org.elasticsearch.xpack.ml.integration.PyTorchModelIT/testInferWithMultipleDocs
**Reproduction line:**
```
gradlew ':x-pack:plugin:ml:qa:native-multi-node-tests:javaRestTest' --tests "org.elasticsearch.xpack.ml.integration.PyTorchModelIT.testInferWithMultipleDocs" -Dtests.seed=E0D151F0DED2B412 -Dtests.locale=ca-ES -Dtests.timezone=America/Montreal -Druntime.java=21
```

**Applicable branches:**
main

**Reproduces locally?:**
Didn't try

**Failure history:**
https://gradle-enterprise.elastic.co/scans/tests?tests.container=org.elasticsearch.xpack.ml.integration.PyTorchModelIT&tests.test=testInferWithMultipleDocs
**Failure excerpt:**
```
java.lang.AssertionError: 2 active tasks found:
internal:index/shard/recovery/start_recovery YDcumwItTqWvln7Kvk5LkA:17655 -                            transport  1696930099813 09:28:19 44.7m       127.0.0.1 javaRestTest-0 recovery of [low_memory_analysis_source_index][7] to {javaRestTest-1}{6XF9PkkYR8GpW47PmXaydA}{czoYWR-xROq8xLJ8x2kjHQ}{javaRestTest-1}{127.0.0.1}{127.0.0.1:63790}{dilm}{8.12.0}{7000099-8500003} [recoveryId=86, targetAllocationId=4vEsDrkWS6qFol7KVThGwA, clusterStateVersion=2460, startingSeqNo=-2, primaryRelocation=false, canDownloadSnapshotFiles=true]
internal:index/shard/recovery/start_recovery qCRYNw1uTX-Vd_NKudrooQ:12297 -                            transport  1696930100318 09:28:20 44.7m       127.0.0.1 javaRestTest-2 recovery of [low_memory_analysis_source_index][6] to {javaRestTest-0}{YDcumwItTqWvln7Kvk5LkA}{PvyMHe6XS6uh4Wag1jfuLA}{javaRestTest-0}{127.0.0.1}{127.0.0.1:63717}{dim}{8.12.0}{7000099-8500003} [recoveryId=84, targetAllocationId=0lxnkFTcScutcVJdpRzG0g, clusterStateVersion=2463, startingSeqNo=-2, primaryRelocation=false, canDownloadSnapshotFiles=true]
 expected:<0> but was:<2>

  at __randomizedtesting.SeedInfo.seed([E0D151F0DED2B412:92CC60B79BA0B63F]:0)
  at org.junit.Assert.fail(Assert.java:88)
  at org.junit.Assert.failNotEquals(Assert.java:834)
  at org.junit.Assert.assertEquals(Assert.java:645)
  at org.elasticsearch.test.rest.ESRestTestCase.lambda$waitForPendingTasks$2(ESRestTestCase.java:506)
  at org.elasticsearch.test.ESTestCase.assertBusy(ESTestCase.java:1196)
  at org.elasticsearch.test.rest.ESRestTestCase.waitForPendingTasks(ESRestTestCase.java:477)
  at org.elasticsearch.test.rest.ESRestTestCase.waitForPendingTasks(ESRestTestCase.java:463)
  at org.elasticsearch.xpack.ml.integration.PyTorchModelRestTestCase.cleanup(PyTorchModelRestTestCase.java:86)
  at jdk.internal.reflect.DirectMethodHandleAccessor.invoke(DirectMethodHandleAccessor.java:103)
  at java.lang.reflect.Method.invoke(Method.java:580)
  at com.carrotsearch.randomizedtesting.RandomizedRunner.invoke(RandomizedRunner.java:1758)
  at com.carrotsearch.randomizedtesting.RandomizedRunner$10.evaluate(RandomizedRunner.java:1004)
  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:1583)

```
test/framework/src/main/java/org/elasticsearch/test/ESTestCase.java
return copyInstance(
            original,
            namedWriteableRegistry,
            StreamOutput::writeNamedWriteable,
            in -> in.readNamedWriteable(categoryClass),
            version
        );
    }
    protected static <T> T copyInstance(
        T original,
        NamedWriteableRegistry namedWriteableRegistry,
        Writeable.Writer<T> writer,
        Writeable.Reader<T> reader,
        TransportVersion version
    ) throws IOException {
        try (BytesStreamOutput output = new BytesStreamOutput()) {
            output.setTransportVersion(version);
            writer.write(output, original);
            try (StreamInput in = new NamedWriteableAwareStreamInput(output.bytes().streamInput(), namedWriteableRegistry)) {
                in.setTransportVersion(version);
                return reader.read(in);
            }
        }
    }
    protected final XContentParserConfiguration parserConfig() {
        XContentParserConfiguration config = XContentParserConfiguration.EMPTY.withRegistry(xContentRegistry())
            .withDeprecationHandler(LoggingDeprecationHandler.INSTANCE);
        return randomBoolean() ? config : config.withRestApiVersion(RestApiVersion.minimumSupported());
    }
    /**