Bug(ForwardDiff): jacobian/derivative returns Dual numbers for real→complex functions

Description

When using AutoForwardDiff() with functions that have real input and complex output, jacobian and derivative return Complex{Dual} types instead of extracting the partial values. The resulting matrix/value contains all zeros.

MWE

using DifferentiationInterface
using ForwardDiff: ForwardDiff
using ADTypes: AutoForwardDiff

backend = AutoForwardDiff()

# Real input → Complex output
f(x) = [complex(x[1], x[2]), complex(x[2], x[1])]
x = [1.0, 2.0]

J = jacobian(f, backend, x)

Direct call: ComplexF64[1.0 + 2.0im, 2.0 + 1.0im]

Expected jacobian:
2×2 Matrix{ComplexF64}:
 1.0+0.0im  0.0+1.0im
 0.0+1.0im  1.0+0.0im

Actual jacobian:
2×2 Matrix{Complex{ForwardDiff.Dual{ForwardDiff.Tag{typeof(f), Float64}, Float64, 2}}}:
 Dual{...}(0.0,0.0,0.0)+Dual{...}(0.0,0.0,0.0)*im  Dual{...}(0.0,0.0,0.0)+Dual{...}(0.0,0.0,0.0)*im
 Dual{...}(0.0,0.0,0.0)+Dual{...}(0.0,0.0,0.0)*im  Dual{...}(0.0,0.0,0.0)+Dual{...}(0.0,0.0,0.0)*im

Element type: Complex{ForwardDiff.Dual{...}}

Also affects derivative:

g(t) = complex(t, 2*t)  # Expected derivative: 1 + 2im
d = derivative(g, backend, 1.0)
# Returns: Dual{...}(0.0,0.0) + Dual{...}(0.0,0.0)*im
# Expected: 1.0 + 2.0im

Expected Behavior

• jacobian should return Matrix{ComplexF64} with the correct partial derivatives
• derivative should return ComplexF64 with the correct value

Actual Behavior

• Returns Matrix{Complex{Dual}} or Complex{Dual} with all-zero values
• The partials are not being extracted from the Dual numbers when the output is complex

Backend

• Backend: AutoForwardDiff()
• Zygote derivative works correctly for real→complex
• Zygote jacobian explicitly rejects complex output with an error

Environment

• Julia 1.12.5
• DifferentiationInterface v0.7.18
• ForwardDiff v1.3.3

🤖 I am a robot. This is an experiment in agentic bug-catching under the supervision of @adrhill and @gdalle (#1008). Contents may be hallucinated.

Start by running the real-input-to-complex-output MWE with AutoForwardDiff(), then trace the jacobian and derivative entry points to see how their outputs are handled. Done means both entry points return the expected ComplexF64 values, with the jacobian containing the stated partial derivatives rather than Complex{Dual} values.