Outsource saving of bounds check errors

[bennibolm]

During subcell IDP limiting, the given subcell bounds can be checked. This happens in the stage callback BoundsCheckCallback. It contains, on the one hand the calculation of the maximum deviation for each variable, and on the other hand, a possible saving of these errors to a txt file.
This PR outsources the saving of the bounds check errors into its own function.

First, this is a much cleaner way to of structuring the bounds check routine.
But mainly, I noticed some very weird behaviors of this bounds check regarding allocations a couple of times in the last months. In some cases, there are many allocs.
And a finally found the reason for that in the error saving lines of code. Sometimes this phenomenon didn't really make sense since save_errors was set to false, but probably there were problems with this sort of IO inside the same routine. Nevertheless, with this variant here, that is solved.

Additionally, this PR increases the coverage by activating saving the bounds check errors for a local limiting and adapts the first time step the deviations should be saved (in 3b513ed).

[github-actions]

Review checklist

This checklist is meant to assist creators of PRs (to let them know what reviewers will typically look for) and reviewers (to guide them in a structured review process). Items do not need to be checked explicitly for a PR to be eligible for merging.

Purpose and scope

• The PR has a single goal that is clear from the PR title and/or description.
• All code changes represent a single set of modifications that logically belong together.
• No more than 500 lines of code are changed or there is no obvious way to split the PR into multiple PRs.

Code quality

• The code can be understood easily.
• Newly introduced names for variables etc. are self-descriptive and consistent with existing naming conventions.
• There are no redundancies that can be removed by simple modularization/refactoring.
• There are no leftover debug statements or commented code sections.
• The code adheres to our conventions and style guide, and to the Julia guidelines.

Documentation

• New functions and types are documented with a docstring or top-level comment.
• Relevant publications are referenced in docstrings (see example for formatting).
• Inline comments are used to document longer or unusual code sections.
• Comments describe intent ("why?") and not just functionality ("what?").
• If the PR introduces a significant change or new feature, it is documented in NEWS.md.

Testing

• The PR passes all tests.
• New or modified lines of code are covered by tests.
• New or modified tests run in less then 10 seconds.

Performance

• There are no type instabilities or memory allocations in performance-critical parts.
• If the PR intent is to improve performance, before/after time measurements are posted in the PR.

Verification

• The correctness of the code was verified using appropriate tests.
• If new equations/methods are added, a convergence test has been run and the results
  are posted in the PR.

Created with ❤️ by the Trixi.jl community.

[codecov]

Codecov Report

Attention: Patch coverage is 96.87500% with 1 lines in your changes are missing coverage. Please review.

Project coverage is 96.15%. Comparing base (c221bca) to head (b590233).

Files	Patch %	Lines
src/callbacks_stage/subcell_bounds_check_2d.jl	96.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1824      +/-   ##
==========================================
+ Coverage   96.09%   96.15%   +0.06%     
==========================================
  Files         453      453              
  Lines       36481    36485       +4     
==========================================
+ Hits        35055    35081      +26     
+ Misses       1426     1404      -22     

Flag	Coverage Δ
unittests	96.15% <96.88%> (+0.06%)	⬆️

Flags with carried forward coverage won't be shown. Click here to find out more.

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

[sloede]

Final changes I think - almost gtg

[sloede]

LGTM once tests pass

[bennibolm]

To complete testing this "Save deviations"-part, I added another test in 8111037.