Add overloaded_inputs for preparations

[ErikQQY]

Fix: #668

This PR only adds the overloaded_inputs functionalities for Jacobian preparations, not sure if the derivative, gradient and hessian preparation need this API.

The tests for this feature maybe too simple, need some suggestions for better test cases.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 97.61%. Comparing base (6604be2) to head (ebc6022).
Report is 1 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main     #672   +/-   ##
=======================================
  Coverage   97.61%   97.61%           
=======================================
  Files         112      114    +2     
  Lines        5609     5619   +10     
=======================================
+ Hits         5475     5485   +10     
  Misses        134      134           

Flag	Coverage Δ
DI	98.76% <100.00%> (+<0.01%)	⬆️
DIT	95.35% <ø> (ø)

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[ErikQQY]

CI failures seem not related.

[gdalle]

Thanks for getting this started! In terms of design, I think we should not just return an eltype but instead we should return the full dualized array. The reason being that some backends (like Mooncake) don't take an elementwise dual.
Could you also make sure that code coverage does not decrease?

[ErikQQY]

All tests passed now.

[ErikQQY]

Also implemented the overloaded_inputs for derivative and gradient preparations.