[Segment Replication] Verify All Integ Tests are Passing with Segment Replication Enabled

[Rishikesh1159]

Describe the bug Currently few server module integ tests fail with segment replication enabled. These failures happen even after introducing a new segrep client (with wait until replica caught up behaviour), more details can be found in #8925. This issue will be used to track all the integ tests failures with segment replication enabled.

This issue is being tracked as a sub task and part of meta issue https://github.com/opensearch-project/OpenSearch/issues/6761

Sub Tasks:

• [x] https://github.com/opensearch-project/OpenSearch/issues/8848
• [x] https://github.com/opensearch-project/OpenSearch/issues/9484
• [x] https://github.com/opensearch-project/OpenSearch/issues/7161
• [x] https://github.com/opensearch-project/OpenSearch/issues/7163
• [x] https://github.com/opensearch-project/OpenSearch/issues/9419

Expected behavior We should have 0 integ tests failing in server module with segment replication enabled.

Plugins Please list all plugins currently enabled.

Screenshots If applicable, add screenshots to help explain your problem.

Host/Environment (please complete the following information):

• OS: [e.g. iOS]
• Version [e.g. 22]

Additional context Add any other context about the problem here.

[dreamer-89]

@Rishikesh1159 : I see all tests mentioned in issue descripted are resolved. Are there more test failures ? If not, can we close this issue