Add integration tests for remote store restore flow (#8484)

[BhumikaSaini-Amazon]

---

Description

Manual backport for #8484

Related Issues

#8483

Check List

• New functionality includes testing.
  • All tests pass
• New functionality has been documented.
  • New functionality has javadoc added
• Commits are signed per the DCO using --signoff
• Commit changes are listed out in CHANGELOG.md file (See: Changelog)

By submitting this pull request, I confirm that my contribution is made under the terms of the Apache 2.0 license.
For more information on following Developer Certificate of Origin and signing off your commits, please check here.

[github-actions]

Gradle Check (Jenkins) Run Completed with:

• RESULT: SUCCESS ✅
• URL: https://build.ci.opensearch.org/job/gradle-check/20643/
• CommitID: 70b5e86

[codecov]

Codecov Report

Merging #8810 (70b5e86) into 2.x (d83147f) will decrease coverage by 0.14%.
The diff coverage is 64.03%.

@@             Coverage Diff              @@
##                2.x    #8810      +/-   ##
============================================
- Coverage     70.80%   70.66%   -0.14%     
+ Complexity    57405    57314      -91     
============================================
  Files          4759     4758       -1     
  Lines        271578   271479      -99     
  Branches      40034    40018      -16     
============================================
- Hits         192283   191847     -436     
- Misses        62795    63164     +369     
+ Partials      16500    16468      -32     

Impacted Files	Coverage Δ
...cluster/reroute/TransportClusterRerouteAction.java	46.05% <0.00%> (+1.31%)	⬆️
...ices/shards/TransportIndicesShardStoresAction.java	4.90% <0.00%> (ø)
...a/org/opensearch/cluster/routing/RoutingTable.java	94.37% <ø> (ø)
...on/lucene/search/function/RandomScoreFunction.java	68.96% <ø> (ø)
...java/org/opensearch/common/recycler/Recyclers.java	91.42% <ø> (ø)
...g/opensearch/common/util/AbstractPagedHashMap.java	71.05% <ø> (ø)
.../java/org/opensearch/common/util/BytesRefHash.java	87.87% <ø> (ø)
.../java/org/opensearch/common/util/LongLongHash.java	92.59% <ø> (ø)
...g/opensearch/common/util/ReorganizingLongHash.java	95.31% <ø> (ø)
.../src/main/java/org/opensearch/gateway/Gateway.java	8.33% <0.00%> (ø)
... and 47 more

... and 440 files with indirect coverage changes

[sachinpkale]

Mostly integ tests were changed in this PR. Bypassing codecov/patch failure.