Implement DifferentiateWith to translate between backends

[gdalle]

Core

• Define DifferentiateWith(f, backend) to force differentiation with a given backend (exported but unstable API)
• Rename backend_string into backend_str

Extensions

• Add ChainRules for DifferentiateWith based on value_and_pushforward + value_and_pullback_split

Tests

• Improve structure of test set and progress logging (group by scenario type)
• Add utility for swapping the function inside a scenario
• Use that to define Zygote-breaking scenarios from the default_scenarios()
• Check that those scenarios don't error when we use AutoZygote() as an outer backend on DifferentiateWith(f, AutoForwardDiff())

Documentation

• Document DifferentiateWith (docstring with example + overview)

[codecov-commenter]

Codecov Report

Attention: Patch coverage is 81.35593% with 11 lines in your changes are missing coverage. Please review.

Project coverage is 95.60%. Comparing base (fac64b7) to head (340bb95).

Files	Patch %	Lines
...erentiationInterfaceTest/src/scenarios/scenario.jl	33.33%	6 Missing ⚠️
...onInterfaceChainRulesCoreExt/differentiate_with.jl	55.55%	4 Missing ⚠️
DifferentiationInterface/src/utils/exceptions.jl	0.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #218      +/-   ##
==========================================
- Coverage   95.83%   95.60%   -0.24%     
==========================================
  Files          70       73       +3     
  Lines        3792     3820      +28     
==========================================
+ Hits         3634     3652      +18     
- Misses        158      168      +10     

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[adrhill]

This one is a hit!