### CI Link

https://gradle-enterprise.elastic.co/s/bettqvfg5kyos

### Repro line

./gradlew ':server:internalClusterTest' --tests "org.elasticsearch.indices.recovery.IndexRecoveryIT.testTransientErrorsDuringRecoveryAreRetried" -Dtests.seed=4BDFC31A406EBDF9 -Dtests.locale=ga -Dtests.timezone=America/Atikokan -Druntime.java=19	

### Does it reproduce?

Didn't try

### Applicable branches

main

### Failure history

https://gradle-enterprise.elastic.co/scans/tests?search.timeZoneId=Europe/Rome&tests.container=org.elasticsearch.indices.recovery.IndexRecoveryIT&tests.test=testTransientErrorsDuringRecoveryAreRetried

### Failure excerpt

```
java.lang.AssertionError: timed out waiting for green state
```

Call to `ensureGreen()` times out before being able to reach a stable cluster state.
server/src/internalClusterTest/java/org/elasticsearch/indices/recovery/IndexRecoveryIT.java
for (NodeStats nodeStats : statsResponse1.getNodes()) {
                final RecoveryStats recoveryStats = nodeStats.getIndices().getRecoveryStats();
                if (nodeStats.getNode().getName().equals(nodeA)) {
                    assertThat(
                        "node A throttling should increase",
                        recoveryStats.throttleTime().millis(),
                        greaterThan(finalNodeAThrottling)
                    );
                }
                if (nodeStats.getNode().getName().equals(nodeB)) {
                    assertThat(
                        "node B throttling should increase",
                        recoveryStats.throttleTime().millis(),
                        greaterThan(finalNodeBThrottling)
                    );
                }
            }
        });
        logger.info("--> speeding up recoveries");
        restoreRecoverySpeed();
        
        ensureGreen();
        response = client().admin().indices().prepareRecoveries(INDEX_NAME).execute().actionGet();
        recoveryStates = response.shardRecoveryStates().get(INDEX_NAME);
        assertThat(recoveryStates.size(), equalTo(1));
        assertRecoveryState(recoveryStates.get(0), 0, PeerRecoverySource.INSTANCE, true, Stage.DONE, nodeA, nodeB);
        validateIndexRecoveryState(recoveryStates.get(0).getIndex());
        Consumer<String> assertNodeHasThrottleTimeAndNoRecoveries = nodeName -> {
            NodesStatsResponse nodesStatsResponse = client().admin()
                .cluster()