[JENKINS-72448] Make sure that logging statements are in correct order

[uhafner]

Use a unique log handler so that all logging statements are shown only once and in the correct order. Also make sure that all log statements are persisted, otherwise the view "coverage/info" shows only a part of the log.

Note: codingstyle v3.31.0 is required as well to correctly show merged error messages in the correct order.

[codecov]

Codecov Report

Attention: 3 lines in your changes are missing coverage. Please review.

Comparison is base (7a14a23) 76.56% compared to head (b36eaa8) 76.56%.

Files	Patch %	Lines
...ugins/coverage/metrics/steps/CoverageReporter.java	95.34%	1 Missing and 1 partial ⚠️
...gins/coverage/metrics/steps/CoverageViewModel.java	0.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff            @@
##               main      #47   +/-   ##
=========================================
  Coverage     76.56%   76.56%           
- Complexity      737      741    +4     
=========================================
  Files            47       47           
  Lines          2628     2633    +5     
  Branches        255      254    -1     
=========================================
+ Hits           2012     2016    +4     
- Misses          532      533    +1     
  Partials         84       84           

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