Fix data stream retrieval in DataStreamAndIndexLifecycleMixingTests

These tests had the potential to fail when two consecutive GET data
streams requests would hit two different nodes, where one node already
had the cluster state that contained the new backing index and the other
node didn't yet.

Caused by #122852

Fixes #124837
Fixes #124849
Fixes #124850
Fixes #124886
Fixes #125083

Author: nielsbauman

muted-tests.yml

@@ -324,27 +324,15 @@ tests:
 - class: org.elasticsearch.common.metrics.ExponentiallyWeightedMovingRateTests
   method: testEwmr_threadSafe
   issue: https://github.com/elastic/elasticsearch/issues/124692
-- class: org.elasticsearch.xpack.ilm.DataStreamAndIndexLifecycleMixingTests
-  method: testUpdateIndexTemplateToDataStreamLifecyclePreference
-  issue: https://github.com/elastic/elasticsearch/issues/124837
 - class: org.elasticsearch.backwards.MixedClusterClientYamlTestSuiteIT
   method: test {p0=search.vectors/41_knn_search_bbq_hnsw/Test knn search}
   issue: https://github.com/elastic/elasticsearch/issues/124848
-- class: org.elasticsearch.xpack.ilm.DataStreamAndIndexLifecycleMixingTests
-  method: testUpdateIndexTemplateToMigrateFromDataStreamLifecycleToIlm
-  issue: https://github.com/elastic/elasticsearch/issues/124849
-- class: org.elasticsearch.xpack.ilm.DataStreamAndIndexLifecycleMixingTests
-  method: testUpdateIndexTemplateFromILMtoBothILMAndDataStreamLifecycle
-  issue: https://github.com/elastic/elasticsearch/issues/124850
 - class: org.elasticsearch.datastreams.lifecycle.ExplainDataStreamLifecycleIT
   method: testExplainLifecycle
   issue: https://github.com/elastic/elasticsearch/issues/124882
 - class: org.elasticsearch.datastreams.lifecycle.ExplainDataStreamLifecycleIT
   method: testSystemExplainLifecycle
   issue: https://github.com/elastic/elasticsearch/issues/124885
-- class: org.elasticsearch.xpack.ilm.DataStreamAndIndexLifecycleMixingTests
-  method: testIndexTemplateSwapsILMForDataStreamLifecycle
-  issue: https://github.com/elastic/elasticsearch/issues/124886
 - class: org.elasticsearch.packaging.test.BootstrapCheckTests
   method: test20RunWithBootstrapChecks
   issue: https://github.com/elastic/elasticsearch/issues/124940
@@ -369,9 +357,6 @@ tests:
 - class: org.elasticsearch.packaging.test.DockerTests
   method: test011SecurityEnabledStatus
   issue: https://github.com/elastic/elasticsearch/issues/124990
-- class: org.elasticsearch.xpack.ilm.DataStreamAndIndexLifecycleMixingTests
-  method: testGetDataStreamResponse
-  issue: https://github.com/elastic/elasticsearch/issues/125083
 - class: org.elasticsearch.packaging.test.DockerTests
   method: test012SecurityCanBeDisabled
   issue: https://github.com/elastic/elasticsearch/issues/116636