ReindexFailureTests fails with in-flight search context

[dnhatn]

ReindexFailureTests suite fails quite often today (see the stats). I could not reproduce this locally.

java.lang.AssertionError: There are still [1] in-flight contexts. The first one's creation site is listed as the cause of this exception.
	at org.elasticsearch.search.MockSearchService.assertNoInFlightContext(MockSearchService.java:51)
	at org.elasticsearch.test.ESTestCase.lambda$ensureAllSearchContextsReleased$6(ESTestCase.java:507)
	at org.elasticsearch.test.ESTestCase.assertBusy(ESTestCase.java:866)
	at org.elasticsearch.test.ESTestCase.assertBusy(ESTestCase.java:840)
	at org.elasticsearch.test.ESTestCase.ensureAllSearchContextsReleased(ESTestCase.java:507)
	at org.elasticsearch.test.ESIntegTestCase.cleanUpCluster(ESIntegTestCase.java:1967)

Some instances:

• https://gradle-enterprise.elastic.co/s/p4cnifsgjc67s
• https://gradle-enterprise.elastic.co/s/7vtrpwj2lqg3y

[elasticmachine]

Pinging @elastic/es-distributed

[henningandersen]

We could be facing this race condition:

https://github.com/elastic/elasticsearch/pull/46060/files#diff-ea35f804425b3f692e93dfef2ea1d1a5R78

though I did not look deeply into this yet.