[Backport 2.x][Tiered Caching] Moving query recomputation logic outside of write lock

[sgup432]

Description

[Describe what this change achieves]

Related Issues

Resolves #14187

Check List

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

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[sgup432]

@sohami @andrross Need help on this one

[github-actions]

❕ Gradle check result for b2e13dd: UNSTABLE

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: Patch coverage is 93.02326% with 3 lines in your changes missing coverage. Please review.

Project coverage is 71.46%. Comparing base (f2d8e1d) to head (b2e13dd).
Report is 1 commits behind head on 2.x.

Files	Patch %	Lines
...search/cache/common/tier/TieredSpilloverCache.java	93.02%	2 Missing and 1 partial ⚠️

Additional details and impacted files

@@             Coverage Diff              @@
##                2.x   #14565      +/-   ##
============================================
+ Coverage     71.39%   71.46%   +0.06%     
- Complexity    62268    62339      +71     
============================================
  Files          5102     5102              
  Lines        293130   293169      +39     
  Branches      42715    42721       +6     
============================================
+ Hits         209275   209508     +233     
+ Misses        66203    66055     -148     
+ Partials      17652    17606      -46     

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[opensearch-trigger-bot]

The backport to 2.x failed:

The process '/usr/bin/git' failed with exit code 128

To backport manually, run these commands in your terminal:

# Fetch latest updates from GitHub
git fetch
# Create a new working tree
git worktree add ../.worktrees/backport-2.x 2.x
# Navigate to the new working tree
pushd ../.worktrees/backport-2.x
# Create a new branch
git switch --create backport/backport-14565-to-2.x
# Cherry-pick the merged commit of this pull request and resolve the conflicts
git cherry-pick -x --mainline 1 d21fd36014c2ccf582b604658387dc08a1d788d9
# Push it to GitHub
git push --set-upstream origin backport/backport-14565-to-2.x
# Go back to the original working tree
popd
# Delete the working tree
git worktree remove ../.worktrees/backport-2.x

Then, create a pull request where the base branch is 2.x and the compare/head branch is backport/backport-14565-to-2.x.