Mooncake for NonlinearSolve's Adjoints.

[AstitvaAggarwal]

Mooncake's tests currently fail due to the pullback in the Chainrule.rrule's adjoint calculation. It does not handle the Tangent types passed in the reverse-pass as used in the Mooncake, ChainRules rule interface (Mooncake.from_chainrules etc).

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

Add any other context about the problem here.