Move FiniteDiffDerivative to test utils, remove from public API

[dpanici]

No description provided.

[github-actions]

Memory benchmark result

|               Test Name                |      %Δ      |    Master (MB)     |      PR (MB)       |    Δ (MB)    |    Time PR (s)     |  Time Master (s)   |
| -------------------------------------- | ------------ | ------------------ | ------------------ | ------------ | ------------------ | ------------------ |
  test_objective_jac_w7x                 |    1.18 %    |     3.888e+03      |     3.934e+03      |    45.87     |       40.47        |       36.53        |
  test_proximal_jac_w7x_with_eq_update   |   -1.77 %    |     6.640e+03      |     6.523e+03      |   -117.26    |       166.64       |       161.38       |
  test_proximal_freeb_jac                |   -0.08 %    |     1.322e+04      |     1.321e+04      |    -11.13    |       85.32        |       83.00        |
  test_proximal_freeb_jac_blocked        |   -0.35 %    |     7.510e+03      |     7.483e+03      |    -26.59    |       75.48        |       73.56        |
  test_proximal_freeb_jac_batched        |   -0.39 %    |     7.507e+03      |     7.478e+03      |    -29.23    |       73.86        |       72.86        |
  test_proximal_jac_ripple               |    1.66 %    |     3.499e+03      |     3.558e+03      |    58.19     |       67.47        |       66.06        |
  test_proximal_jac_ripple_bounce1d      |    1.39 %    |     3.544e+03      |     3.593e+03      |    49.29     |       76.71        |       77.02        |
  test_eq_solve                          |    0.18 %    |     2.027e+03      |     2.031e+03      |     3.67     |       94.51        |       94.87        |

For the memory plots, go to the summary of Memory Benchmarks workflow and download the artifact.

[YigitElma]

I think during the dev meeting, we decided to keep the backend flexible for other autodiff libraries, so I think the conditional if use_jax is still useful. To be honest, I think that is a very distant future (so not very important for now) but everywhere in the code, we omit importing jax directly, so for consistency, having the conditional is better imo.

[dpanici]

Ah right sorry, I will revert that

[codecov]

Codecov Report

❌ Patch coverage is 66.66667% with 1 line in your changes missing coverage. Please review.
✅ Project coverage is 94.53%. Comparing base (29c7877) to head (6f3290f).

Files with missing lines	Patch %	Lines
desc/derivatives.py	66.66%	1 Missing ⚠️

Additional details and impacted files

@@           Coverage Diff            @@
##           master    #2094    +/-   ##
========================================
  Coverage   94.52%   94.53%            
========================================
  Files         102      102            
  Lines       28785    28654   -131     
========================================
- Hits        27210    27087   -123     
+ Misses       1575     1567     -8     

Files with missing lines	Coverage Δ
desc/derivatives.py	94.54% <66.66%> (-0.48%)	⬇️

... and 3 files with indirect coverage changes

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[ddudt]

I still think we could remove the FiniteDiffDerivative class completely and replace it with something simpler, since it is only used in the testing functions. But this is fine for now.