CI: SearchableSnapshotsBlobStoreCacheIntegTests testBlobStoreCache failure

[nik9000]

Build scan:
https://gradle-enterprise.elastic.co/s/x2jjcc4jufimu

Repro line:

./gradlew ':x-pack:plugin:searchable-snapshots:test' \
  --tests "org.elasticsearch.blobstore.cache.SearchableSnapshotsBlobStoreCacheIntegTests.testBlobStoreCache" \
  -Dtests.seed=CC89BE29420C144B -Dtests.security.manager=true -Dtests.locale=fr-CH \
  -Dtests.timezone=Pacific/Apia -Druntime.java=14 -Dtests.fips.enabled=true

Reproduces locally?:
Nope.

Applicable branches:
7.x

Failure history:
https://build-stats.elastic.co/goto/4b69af8574c4548e11c08a824c38f3e7

Failed five times in the past week and never before.

Failure excerpt:

org.elasticsearch.blobstore.cache.SearchableSnapshotsBlobStoreCacheIntegTests > testBlobStoreCache FAILED
    java.lang.AssertionError: timed out waiting for green state
        at org.junit.Assert.fail(Assert.java:88)
        at org.elasticsearch.test.ESIntegTestCase.ensureColor(ESIntegTestCase.java:952)
        at org.elasticsearch.test.ESIntegTestCase.ensureGreen(ESIntegTestCase.java:905)
        at org.elasticsearch.test.ESIntegTestCase.ensureGreen(ESIntegTestCase.java:894)
        at org.elasticsearch.blobstore.cache.SearchableSnapshotsBlobStoreCacheIntegTests.testBlobStoreCache(SearchableSnapshotsBlobStoreCacheIntegTests.java:146)

    java.lang.AssertionError: ClusterHealthResponse has timed out - returned: [{"cluster_name":"SUITE-TEST_WORKER_VM=[843]-CLUSTER_SEED=[-2553043917039051597]-HASH=[24B456B2CB3]-cluster","status":"green","timed_out":true,"number_of_nodes":5,"number_of_data_nodes":1,"active_primary_shards":5,"active_shards":5,"relocating_shards":0,"initializing_shards":0,"unassigned_shards":0,"delayed_unassigned_shards":0,"number_of_pending_tasks":0,"number_of_in_flight_fetch":0,"task_max_waiting_in_queue_millis":0,"active_shards_percent_as_number":100.0}]
    Expected: is <false>
         but: was <true>
        at org.hamcrest.MatcherAssert.assertThat(MatcherAssert.java:18)
        at org.elasticsearch.test.hamcrest.ElasticsearchAssertions.assertNoTimeout(ElasticsearchAssertions.java:111)
        at org.elasticsearch.test.ESIntegTestCase.ensureClusterSizeConsistency(ESIntegTestCase.java:1050)
        at org.elasticsearch.test.ESIntegTestCase.afterInternal(ESIntegTestCase.java:575)
        at org.elasticsearch.test.ESIntegTestCase.cleanUpCluster(ESIntegTestCase.java:2233)
        at java.base/jdk.internal.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
        at java.base/jdk.internal.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)
        at java.base/jdk.internal.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)
        at java.base/java.lang.reflect.Method.invoke(Method.java:564)
        at com.carrotsearch.randomizedtesting.RandomizedRunner.invoke(RandomizedRunner.java:1750)
        at com.carrotsearch.randomizedtesting.RandomizedRunner$10.evaluate(RandomizedRunner.java:996)
        at com.carrotsearch.randomizedtesting.rules.StatementAdapter.evaluate(StatementAdapter.java:36)

[elasticmachine]

Pinging @elastic/es-distributed (:Distributed/Snapshot/Restore)

[elasticmachine]

Pinging @elastic/es-core-infra (:Core/Infra/Build)

[tlrx]

This failure is due to a bug in system indices for which I opened #61785. Build stats also show more failures that are likely caused by a change in build plugins, for which I opened #61888.