Update to DifferentiationInterface v0.6

[gdalle]

Checklist

• Appropriate tests were added
• Any code changes were done in a way that does not break public API
• All documentation related to code changes were updated
• The new code follows the
  contributor guidelines, in particular the SciML Style Guide and
  COLPRAC.
• Any new documentation only uses public API

Additional context

Following the recent release of DI v0.6, here are some changes that need to happen in OptimizationBase (supersedes #107):

• Move the extras (now called prep) before the ADTypes backend object in every operator call
• Refactor all pushforward, pullback and hvp calls to use tuples for their tangents
• Do the same for all extensions (why are they still here?)
• Use Constant context arguments for the Hessian

We also need to perform the following changes to accommodate Enzyme v0.13:

• Annotate function in autodiff_deferred

[gdalle]

@Vaibhavdixit02 do you think you can take it from here?

[Vaibhavdixit02]

Yup I got it, thanks a lot for starting this!