Cleanup SystemIndexTests with RunAsSubjectClient

[cwperks]

Description

This PR is a follow-up to #4896 that borrows the RunAsSubjectClient concept from opensearch-project/OpenSearch#16976 and shows how an IdentityAwarePlugin can use the pluginSubject that its been assigned to initialize a client wrapper that can be used for SystemIndexAccess.

This PR only contains test changes.

• Category (Enhancement, New feature, Bug fix, Test fix, Refactoring, Maintenance, Documentation)

Test refactor

Check List

• New functionality includes testing
• New functionality has been documented
• New Roles/Permissions have a corresponding security dashboards plugin PR
• API changes companion pull request created
• Commits are signed per the DCO using --signoff

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.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 71.49%. Comparing base (1924e41) to head (0952ac5).
Report is 1 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #5027      +/-   ##
==========================================
- Coverage   71.50%   71.49%   -0.01%     
==========================================
  Files         336      336              
  Lines       22625    22625              
  Branches     3598     3598              
==========================================
- Hits        16178    16176       -2     
- Misses       4648     4653       +5     
+ Partials     1799     1796       -3     

see 5 files with indirect coverage changes

[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:

# Navigate to the root of your repository
cd $(git rev-parse --show-toplevel)
# Fetch latest updates from GitHub
git fetch
# Create a new working tree
git worktree add ../.worktrees/security/backport-2.x 2.x
# Navigate to the new working tree
pushd ../.worktrees/security/backport-2.x
# Create a new branch
git switch --create backport/backport-5027-to-2.x
# Cherry-pick the merged commit of this pull request and resolve the conflicts
git cherry-pick -x --mainline 1 5e5339d39b80297ca2e9411854fbca4440d5d51c
# Push it to GitHub
git push --set-upstream origin backport/backport-5027-to-2.x
# Go back to the original working tree
popd
# Delete the working tree
git worktree remove ../.worktrees/security/backport-2.x

Then, create a pull request where the base branch is 2.x and the compare/head branch is backport/backport-5027-to-2.x.

[cwperks]

Backport for this change will be included in #5028