fix: ensure proper cleanup of processes in wrap_litserve_start

[bhimrazy]

What does this PR do?

This PR implements proper cleanup of processes initiated by wrap_litserve_start, ensuring that test cases using this function exit gracefully upon completion.

Fixes #431

Before submitting

• Was this discussed/agreed via a Github issue? (no need for typos and docs improvements)
• Did you read the contributor guideline, Pull Request section?
• Did you make sure to update the docs?
• Did you write any new necessary tests?

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[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 89%. Comparing base (49cedbd) to head (6c0aff8).
Report is 1 commits behind head on main.

Additional details and impacted files

@@         Coverage Diff         @@
##           main   #432   +/-   ##
===================================
  Coverage    89%    89%           
===================================
  Files        31     31           
  Lines      2025   2027    +2     
===================================
+ Hits       1806   1813    +7     
+ Misses      219    214    -5     

[aniketmaurya]

Thanks a lot @bhimrazy 🚀