refactor(log): replace protected properties with Symbols

[timreichen]

Changes
This PR replaces protected properties with Symbols.

Reasoning
Either the properties should be public and not have an underscore or private and thus not accessible.

[codecov]

Codecov Report

Attention: Patch coverage is 98.55072% with 1 line in your changes missing coverage. Please review.

Project coverage is 96.26%. Comparing base (75cb767) to head (2cca4b6).
Report is 3 commits behind head on main.

Files	Patch %	Lines
log/file_handler.ts	97.50%	1 Missing ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #5724   +/-   ##
=======================================
  Coverage   96.26%   96.26%           
=======================================
  Files         477      478    +1     
  Lines       38512    38541   +29     
  Branches     5589     5589           
=======================================
+ Hits        37072    37102   +30     
+ Misses       1398     1397    -1     
  Partials       42       42           

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[kt3k]

LGTM