Make ClassicSovlerInit use backward transitions and completely remove `smooth!` from the package

[nathanaelbosch]

Solves #259

Maybe do some benchmarks again before merging, just to see if/how this influenced performance

[codecov[bot]]

Codecov Report

Merging #262 (ba7d92f) into main (e627234) will decrease coverage by 0.36%. Report is 4 commits behind head on main. The diff coverage is 100.00%.

@@            Coverage Diff             @@
##             main     #262      +/-   ##
==========================================
- Coverage   95.75%   95.40%   -0.36%     
==========================================
  Files          35       35              
  Lines        1462     1435      -27     
==========================================
- Hits         1400     1369      -31     
- Misses         62       66       +4     

Files	Coverage Δ
src/filtering/smooth.jl	100.00% <ø> (ø)
src/initialization/classicsolverinit.jl	97.40% <100.00%> (+0.10%)	:arrow_up:

... and 3 files with indirect coverage changes

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[nathanaelbosch]

Held up by Fenrir.jl's patch release with increased ProbNumDiffEq.jl compat: https://github.com/JuliaRegistries/General/pull/94415