Add Batched Nonlinear Solvers and Forward AD rules

[avik-pal]

No description provided.

[codecov]

Codecov Report

Attention: Patch coverage is 79.83871% with 25 lines in your changes are missing coverage. Please review.

Project coverage is 72.70%. Comparing base (54b894e) to head (a37f694).
Report is 2 commits behind head on main.

Files	Patch %	Lines
ext/BatchedRoutinesReverseDiffExt.jl	0.00%	6 Missing ⚠️
...dRoutinesSciMLSensitivityExt/steadystateadjoint.jl	86.66%	6 Missing ⚠️
src/nlsolve/utils.jl	66.66%	5 Missing ⚠️
src/api.jl	50.00%	4 Missing ⚠️
src/helpers.jl	0.00%	2 Missing ⚠️
...BatchedRoutinesForwardDiffExt/nonlinearsolve_ad.jl	95.83%	1 Missing ⚠️
src/nlsolve/batched_raphson.jl	93.75%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #13      +/-   ##
==========================================
+ Coverage   71.44%   72.70%   +1.26%     
==========================================
  Files          18       24       +6     
  Lines         872      982     +110     
==========================================
+ Hits          623      714      +91     
- Misses        249      268      +19     

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