Fix suite scope random initializaation (#37163)

The initialization of a suite scope cluster had some sideffects on
subsequent runs which causes issues when tests must be reproduced.
This moves the suite scope initialization to a privte random context.

Closes #36202

test/framework/src/main/java/org/elasticsearch/test/ESIntegTestCase.java

@@ -373,18 +373,24 @@ public abstract class ESIntegTestCase extends ESTestCase {
 
     protected final void beforeInternal() throws Exception {
         final Scope currentClusterScope = getCurrentClusterScope();
+        Callable<Void> setup = () -> {
+            cluster().beforeTest(random(), getPerTestTransportClientRatio());
+            cluster().wipe(excludeTemplates());
+            randomIndexTemplate();
+            return null;
+        };
         switch (currentClusterScope) {
             case SUITE:
                 assert SUITE_SEED != null : "Suite seed was not initialized";
                 currentCluster = buildAndPutCluster(currentClusterScope, SUITE_SEED);
+                RandomizedContext.current().runWithPrivateRandomness(SUITE_SEED, setup);
                 break;
             case TEST:
                 currentCluster = buildAndPutCluster(currentClusterScope, randomLong());
+                setup.call();
                 break;
         }
-        cluster().beforeTest(random(), getPerTestTransportClientRatio());
-        cluster().wipe(excludeTemplates());
-        randomIndexTemplate();
+
     }
 
     private void printTestMessage(String message) {

test/framework/src/test/java/org/elasticsearch/test/test/SuiteScopeClusterIT.java

@@ -41,7 +41,6 @@ public class SuiteScopeClusterIT extends ESIntegTestCase {
     @Test
     @SuppressForbidden(reason = "repeat is a feature here")
     @Repeat(iterations = 10, useConstantSeed = true)
-    @AwaitsFix(bugUrl = "https://github.com/elastic/elasticsearch/issues/36202")
     public void testReproducible() throws IOException {
         if (ITER++ == 0) {
             CLUSTER_SEED = cluster().seed();