### 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
.prepareNodesStats()
            .clear()
            .setIndices(new CommonStatsFlags(CommonStatsFlags.Flag.Recovery))
            .get();
        long nodeAThrottling = Long.MAX_VALUE;
        long nodeBThrottling = Long.MAX_VALUE;
        for (NodeStats nodeStats : statsResponse.getNodes()) {
            final RecoveryStats recoveryStats = nodeStats.getIndices().getRecoveryStats();
            if (nodeStats.getNode().getName().equals(nodeA)) {
                assertThat("node A should have ongoing recovery as source", recoveryStats.currentAsSource(), equalTo(1));
                assertThat("node A should not have ongoing recovery as target", recoveryStats.currentAsTarget(), equalTo(0));
                nodeAThrottling = recoveryStats.throttleTime().millis();
            }
            if (nodeStats.getNode().getName().equals(nodeB)) {
                assertThat("node B should not have ongoing recovery as source", recoveryStats.currentAsSource(), equalTo(0));
                assertThat("node B should have ongoing recovery as target", recoveryStats.currentAsTarget(), equalTo(1));
                nodeBThrottling = recoveryStats.throttleTime().millis();
            }
        }
        logger.info("--> checking throttling increases");
        final long finalNodeAThrottling = nodeAThrottling;
        final long finalNodeBThrottling = nodeBThrottling;
        assertBusy(() -> {
            NodesStatsResponse statsResponse1 = client().admin()
                .cluster()
                .prepareNodesStats()
                .clear()
                .setIndices(new CommonStatsFlags(CommonStatsFlags.Flag.Recovery))
                .get();
            assertThat(statsResponse1.getNodes(), hasSize(2));