Initializing improved differentiation interface

[KnutAM]

Need to add more tests as no changes was required, specifically for diff with state variables + stress iterations

[codecov]

Codecov Report

❌ Patch coverage is 96.25000% with 3 lines in your changes missing coverage. Please review.
✅ Project coverage is 96.16%. Comparing base (56da0ea) to head (888af92).
⚠️ Report is 7 commits behind head on main.

Files with missing lines	Patch %	Lines
src/differentiation.jl	95.91%	2 Missing ⚠️
src/stressiterations.jl	95.83%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #16      +/-   ##
==========================================
- Coverage   97.05%   96.16%   -0.90%     
==========================================
  Files           4        5       +1     
  Lines         204      287      +83     
==========================================
+ Hits          198      276      +78     
- Misses          6       11       +5     

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