src: rename private fields to follow naming convention

[iknoom]

This PR renames ProcessRunner class private fields to follow the snake_case_ naming convention, as specified in doc/contributing/cpp-style-guide.md

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 88.25%. Comparing base (97e55f8) to head (0436e0e).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main   #59923      +/-   ##
==========================================
- Coverage   88.27%   88.25%   -0.03%     
==========================================
  Files         703      703              
  Lines      207333   207333              
  Branches    39875    39872       -3     
==========================================
- Hits       183028   182983      -45     
- Misses      16263    16309      +46     
+ Partials     8042     8041       -1     

Files with missing lines	Coverage Δ
src/node_task_runner.cc	89.32% <100.00%> (ø)

... and 36 files with indirect coverage changes

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