### 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
logger.info("--> move shard from: {} to: {}", nodeA, nodeB);
        client().admin()
            .cluster()
            .prepareReroute()
            .add(new MoveAllocationCommand(INDEX_NAME, 0, nodeA, nodeB))
            .execute()
            .actionGet()
            .getState();
        logger.info("--> waiting for recovery to start both on source and target");
        final Index index = resolveIndex(INDEX_NAME);
        assertBusy(() -> {
            IndicesService indicesService = internalCluster().getInstance(IndicesService.class, nodeA);
            assertThat(indicesService.indexServiceSafe(index).getShard(0).recoveryStats().currentAsSource(), equalTo(1));
            indicesService = internalCluster().getInstance(IndicesService.class, nodeB);
            assertThat(indicesService.indexServiceSafe(index).getShard(0).recoveryStats().currentAsTarget(), equalTo(1));
        });
        logger.info("--> request recoveries");
        RecoveryResponse response = client().admin().indices().prepareRecoveries(INDEX_NAME).execute().actionGet();
        List<RecoveryState> recoveryStates = response.shardRecoveryStates().get(INDEX_NAME);
        List<RecoveryState> nodeARecoveryStates = findRecoveriesForTargetNode(nodeA, recoveryStates);
        assertThat(nodeARecoveryStates.size(), equalTo(1));
        List<RecoveryState> nodeBRecoveryStates = findRecoveriesForTargetNode(nodeB, recoveryStates);
        assertThat(nodeBRecoveryStates.size(), equalTo(1));
        assertRecoveryState(nodeARecoveryStates.get(0), 0, RecoverySource.EmptyStoreRecoverySource.INSTANCE, true, Stage.DONE, null, nodeA);
        validateIndexRecoveryState(nodeARecoveryStates.get(0).getIndex());
        assertOnGoingRecoveryState(nodeBRecoveryStates.get(0), 0, PeerRecoverySource.INSTANCE, true, nodeA, nodeB);
        validateIndexRecoveryState(nodeBRecoveryStates.get(0).getIndex());
        logger.info("--> request node recovery stats");
        NodesStatsResponse statsResponse = client().admin()
            .cluster()