Inconsistency in handling empty arguments

When differentiating with respect to an empty array, the results tend to vary:

using DifferentiationInterface, ForwardDiff, ReverseDiff, Mooncake, Enzyme

ADTYPES = [
    AutoForwardDiff(),
    AutoReverseDiff(),
    AutoMooncake(; config=nothing),
    AutoEnzyme(; mode=Forward),
    AutoEnzyme(; mode=Reverse),
    # and more...
]

for adtype in ADTYPES
    DifferentiationInterface.value_and_gradient(sum, adtype, Float64[])
end

ReverseDiff, Mooncake, and reverse Enzyme all happily return (0.0, []) 😄

Forward Enzyme tries to use a batch size of 0 and errors:

https://github.com/JuliaDiff/DifferentiationInterface.jl/blob/6a58124902a9cc3e623014db28eacd4b56ba4434/DifferentiationInterface/ext/DifferentiationInterfaceEnzymeExt/utils.jl#L11-L14

And ForwardDiff tries to construct a GradientResult which errors:

https://github.com/JuliaDiff/DifferentiationInterface.jl/blob/6a58124902a9cc3e623014db28eacd4b56ba4434/DifferentiationInterface/ext/DifferentiationInterfaceForwardDiffExt/onearg.jl#L315-L318

https://github.com/JuliaDiff/DiffResults.jl/blob/fcf7858d393f0597fc74e195ed46f7bcbe5ff66c/src/DiffResults.jl#L64-L65

Funnily enough gradient with ForwardDiff (rather than value_and_gradient) is fine because it doesn't try to construct the GradientResult. I imagine the other operators would also have varying behaviour.

I suppose it is a bit of a trivial edge case, but would it be possible to unify the behaviour of the AD backends?

Start with the linked empty-argument handling in DifferentiationInterface/ext/DifferentiationInterfaceEnzymeExt/utils.jl and DifferentiationInterface/ext/DifferentiationInterfaceForwardDiffExt/onearg.jl, then run the provided value_and_gradient example across the listed backends. Done means the affected backends and operators have deliberately consistent behavior for empty arguments.