Add Mooncake to Alternative AD Frontends

[willtebbutt]

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

Follow up PR from SciML/DiffEqBase.jl#1103

I've put the rules needed for this to work in src/tmp_mooncake_rules.jl for the sake of debugging. Once we're happy that this is basically good, I'll move this over to an extension in DiffEqBase.

There are currently a few tests which are broken that I don't believe ought to be broken, which I can work on fixing.

It would be helpful to have feedback on whether I've extended the test suite in the right way etc, and to know which bits of the docs I should update (if any).

Thanks!