StaticArrays need opt-in friendly tangent type for Mooncake

[yebai]

DI/DIT requires the following Mooncake opt-in for its StaticArrays-related tests to pass:

function Mooncake.friendly_tangent_cache(x::StaticArray)
    return Mooncake.FriendlyTangentCache{Mooncake.AsPrimal}(copy(x))
end

With this in place, DI’s full test suite passes for Mooncake. That said, it is somewhat unusual that StaticArrays are included as part of DI’s core test suite, since they are not universally supported across AD backends.

DI currently states:

Thorough validation on standard inputs and outputs (numbers, vectors, matrices)

This phrasing is overly broad. In practice, support depends on specific concrete subtypes of Number, AbstractVector, and AbstractMatrix. For instance, Mooncake does not currently support differentiation with BigFloat or Vector{BigFloat}, and similar limitations likely exist for other AD backends.

Related: SciML/ComponentArrays.jl#350

[yolhan83]

Would be type piracy, should be in Mooncake extension since Static Arrays is a standard library and won't accept any extension.
The other way would be for DI to have its own way of converting to and from Mooncake tangents and not rely on friendly tangents but that would be double engennering for almost no reason.
Also if Mooncake makes friendly tangents the default we're back to the same problem.