[Backport 2.x] Create separate transport action for render search template action (#11170)

[cwperks]

Backport #11170 to 2.x

[github-actions]

Compatibility status:

Checks if related components are compatible with change 69e6bba

Incompatible components

Incompatible components: [https://github.com/opensearch-project/security-analytics.git]

Skipped components

Compatible components

Compatible components: [https://github.com/opensearch-project/observability.git, https://github.com/opensearch-project/security.git, https://github.com/opensearch-project/custom-codecs.git, https://github.com/opensearch-project/job-scheduler.git, https://github.com/opensearch-project/cross-cluster-replication.git, https://github.com/opensearch-project/sql.git, https://github.com/opensearch-project/asynchronous-search.git, https://github.com/opensearch-project/notifications.git, https://github.com/opensearch-project/ml-commons.git, https://github.com/opensearch-project/anomaly-detection.git, https://github.com/opensearch-project/reporting.git, https://github.com/opensearch-project/neural-search.git, https://github.com/opensearch-project/index-management.git, https://github.com/opensearch-project/common-utils.git, https://github.com/opensearch-project/alerting.git, https://github.com/opensearch-project/geospatial.git, https://github.com/opensearch-project/k-nn.git, https://github.com/opensearch-project/performance-analyzer-rca.git, https://github.com/opensearch-project/performance-analyzer.git]

[github-actions]

❕ Gradle check result for 69e6bba: UNSTABLE

• TEST FAILURES:

      1 org.opensearch.remotestore.RemoteIndexPrimaryRelocationIT.testPrimaryRelocationWhileIndexing
      1 org.opensearch.backwards.MixedClusterClientYamlTestSuiteIT.test {p0=pit/10_basic/Delete all}

Please review all flaky tests that succeeded after retry and create an issue if one does not already exist to track the flaky failure.

[codecov]

Codecov Report

Attention: 11 lines in your changes are missing coverage. Please review.

Comparison is base (7f7aa05) 71.13% compared to head (69e6bba) 71.07%.

Files	Patch %	Lines
...script/mustache/TransportSearchTemplateAction.java	0.00%	5 Missing ⚠️
...ch/script/mustache/RenderSearchTemplateAction.java	0.00%	3 Missing ⚠️
.../mustache/TransportRenderSearchTemplateAction.java	0.00%	2 Missing ⚠️
...cript/mustache/RestRenderSearchTemplateAction.java	0.00%	1 Missing ⚠️

Additional details and impacted files

@@             Coverage Diff              @@
##                2.x   #11589      +/-   ##
============================================
- Coverage     71.13%   71.07%   -0.07%     
+ Complexity    59325    59216     -109     
============================================
  Files          4881     4883       +2     
  Lines        279290   279300      +10     
  Branches      40933    40933              
============================================
- Hits         198686   198502     -184     
- Misses        63779    63942     +163     
- Partials      16825    16856      +31     

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