Revise integrator interface (again)

[michakraus]

No description provided.

[codecov]

Codecov Report

Attention: Patch coverage is 96.04317% with 66 lines in your changes missing coverage. Please review.

Project coverage is 61.44%. Comparing base (2068b06) to head (404e8e0).
Report is 1 commits behind head on main.

Files	Patch %	Lines
src/projections/cache.jl	71.79%	11 Missing ⚠️
src/integrators/rk/integrators_irk_implicit.jl	80.39%	10 Missing ⚠️
src/spark/integrators_vspark.jl	91.46%	7 Missing ⚠️
src/extrapolation/hermite.jl	73.91%	6 Missing ⚠️
src/spark/integrators_spark.jl	91.89%	6 Missing ⚠️
src/spark/integrators_spark_parameters.jl	0.00%	5 Missing ⚠️
src/integrators/integrator.jl	92.98%	4 Missing ⚠️
src/integrators/integrator_cache.jl	25.00%	3 Missing ⚠️
src/spark/integrators_hspark_secondary.jl	96.55%	3 Missing ⚠️
src/spark/integrators_hspark.jl	96.15%	2 Missing ⚠️
... and 9 more

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #185      +/-   ##
==========================================
- Coverage   62.95%   61.44%   -1.51%     
==========================================
  Files         117      116       -1     
  Lines        8030     7898     -132     
==========================================
- Hits         5055     4853     -202     
- Misses       2975     3045      +70     

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