feat: Add forward mode Mooncake

[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

Warning

Do not merge yet

This PR adds the AutoMooncakeForward type, in anticipation of chalk-lab/Mooncake.jl#389 landing. It is different from the existing AutoMooncake because otherwise we would have had to replace mode(::AutoMooncake) = ForwardMode() with mode(::AutoMooncake) = ForwardOrReverseMode(), which can be considered breaking.

Right now I'm using this branch to experiment with DI integration and finalize tests on the Mooncake side. We'll merge it once we know everything is ready to roll.

cc @willtebbutt