[Backport 2.x] [Remote State] Upload incremental cluster state on master re-election (#15145)

[shiv0408]

backport cbdcbb7 from #15145

[github-actions]

✅ Gradle check result for 21ec4d2: SUCCESS

[codecov]

Codecov Report

Attention: Patch coverage is 67.41573% with 29 lines in your changes missing coverage. Please review.

Project coverage is 71.62%. Comparing base (076e7cb) to head (21ec4d2).
Report is 2 commits behind head on 2.x.

Files with missing lines	Patch %	Lines
...arch/gateway/remote/RemoteClusterStateService.java	20.00%	9 Missing and 3 partials ⚠️
...luster/coordination/RemoteStatePublishRequest.java	36.36%	7 Missing ⚠️
...search/cluster/coordination/CoordinationState.java	83.87%	2 Missing and 3 partials ⚠️
.../java/org/opensearch/gateway/GatewayMetaState.java	83.33%	0 Missing and 4 partials ⚠️
...ster/coordination/PublicationTransportHandler.java	87.50%	1 Missing ⚠️

Additional details and impacted files

@@             Coverage Diff              @@
##                2.x   #15853      +/-   ##
============================================
- Coverage     71.62%   71.62%   -0.01%     
- Complexity    64501    64508       +7     
============================================
  Files          5263     5264       +1     
  Lines        301919   301985      +66     
  Branches      43947    43963      +16     
============================================
+ Hits         216261   216287      +26     
- Misses        67521    67664     +143     
+ Partials      18137    18034     -103     

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