Batched pushforward, pullback and hvp

[gdalle]

DI source

• Define Batch{B,T} to wrap an NTuple, and pick_batchsize(backend, n)
• Implement batched versions of pushforward, pullback and hvp (the seed dx/dy is a Batch, and the result too)
• Completely revamp dense Jacobian and Hessian to use batched operators
• Completely revamp sparse Jacobian and Hessian to use batched operators
• Pick batch size based on the dense backend for Jacobian, or dense outer backend for Hessian
• Reduce code duplication in Jacobian between f and f! by splatting f_or_f!y
• Define internal backends AutoForwardFromPrimitive and AutoReverseFromPrimitive to pretend that a given backend only defines value_and_pushforward / value_and_pullback => tests our entire cascade of fallbacks

DI extensions

• Implement DI.pick_batchsize with ForwardDiff's internal mechanism
• Use pick_batchsize in Enzyme extension
• Use forward-over-reverse for batched HVP in Zygote extension (reverse over reverse made Julia lag forever)

DI tests

• Test our entire cascade of fallbacks with
  • AutoForwardFromPrimitive + ForwardDiff
  • AutoReverseFromPrimitive + ReverseDiff

TODO (in another PR) => see #312

• Test Batch struct / pick_batchsize
• Check type stability and performance
• Test batched versions of the operators for themselves, and not only as part of jacobian or hessian (will be easier thanks to Revamp test scenarios #323)
• Implement batched mode in ForwardDiff and Enzyme extensions (+ maybe FiniteDiff?)

[codecov-commenter]

Codecov Report

Attention: Patch coverage is 98.57820% with 6 lines in your changes missing coverage. Please review.

Project coverage is 96.51%. Comparing base (004e934) to head (e6c05f1).

Files	Patch %	Lines
DifferentiationInterface/src/sparse/jacobian.jl	98.23%	2 Missing ⚠️
...dDiffExt/DifferentiationInterfaceForwardDiffExt.jl	75.00%	1 Missing ⚠️
...fferentiationInterface/src/first_order/jacobian.jl	98.96%	1 Missing ⚠️
...fferentiationInterface/src/second_order/hessian.jl	96.55%	1 Missing ⚠️
DifferentiationInterface/src/sparse/hessian.jl	97.43%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #320      +/-   ##
==========================================
+ Coverage   96.48%   96.51%   +0.03%     
==========================================
  Files          95       96       +1     
  Lines        4435     4564     +129     
==========================================
+ Hits         4279     4405     +126     
- Misses        156      159       +3     

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