Print Analysis in Full Precision to File

[DanielDoehring]

As Float64 is the default type, we should IMO also use default Float64 precision when writing to file.
Ideally, this would also be fully type-generalized.

[github-actions]

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[codecov]

Codecov Report

Attention: Patch coverage is 84.21053% with 3 lines in your changes missing coverage. Please review.

Project coverage is 96.37%. Comparing base (07f960f) to head (55cf90c).
Report is 2 commits behind head on main.

Files with missing lines	Patch %	Lines
src/callbacks_step/analysis.jl	84.21%	3 Missing ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #2155   +/-   ##
=======================================
  Coverage   96.37%   96.37%           
=======================================
  Files         480      480           
  Lines       38178    38178           
=======================================
  Hits        36793    36793           
  Misses       1385     1385           

Flag	Coverage Δ
unittests	96.37% <84.21%> (ø)

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[ranocha]

When this PR is ready to be reviewed, please post an example output and request my review.