Mooncake for AD backend integration - 2

[AstitvaAggarwal]

• Handles Batching Integral Function case for Adjoints
• Nested AD + tests.

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.

[AstitvaAggarwal]

Integrals should be good to handle completely via Mooncake now. note that the Nested AD stuff also requires some @zero_derivative declarations that have been added in chalk-lab/Mooncake.jl#1135, but this PR, nested AD tests are not bounded by a new Mooncake minor release as the nested AD tests only trigger for appropriate Mooncake versions

[AstitvaAggarwal]

for reference this completed part 4 (Integrals) of SciML/SciMLSensitivity.jl#1279 (comment)