Add Search Phase Result Processors to SearchPipelineInfo

[owaiskazi19]

Description

Follow up of #18363

Related Issues

Failed build on neural search side: https://github.com/opensearch-project/neural-search/actions/runs/15329740172/job/43133281587?pr=1360

Check List

• Functionality includes testing.
• API changes companion pull request created, if applicable.
• Public documentation issue/PR created, if applicable.

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[owaiskazi19]

@msfroh missed adding the search phase result processors to info failed build on neural search side. Mind taking a look?

[github-actions]

✅ Gradle check result for 51f2d37: SUCCESS

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 72.58%. Comparing base (fe4a98d) to head (51f2d37).
Report is 5 commits behind head on main.

Additional details and impacted files

@@             Coverage Diff              @@
##               main   #18400      +/-   ##
============================================
- Coverage     72.60%   72.58%   -0.03%     
- Complexity    67682    67686       +4     
============================================
  Files          5497     5497              
  Lines        311819   311823       +4     
  Branches      45265    45265              
============================================
- Hits         226409   226339      -70     
- Misses        66941    67026      +85     
+ Partials      18469    18458      -11     

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