  The recent discovery of intrinsic supercurrent diode effect, and its prompt
observation in a rich variety of systems, has shown that nonreciprocal
supercurrents naturally emerge when both space- and time-inversion symmetries
are broken. In Josephson junctions, nonreciprocal supercurrent can be
conveniently described in terms of spin-split Andreev states. Here, we
demonstrate a sign reversal of the supercurrent diode effect, in both its AC
and DC manifestations. In particular, the AC diode effect -- i.e., the
asymmetry of the Josephson inductance as a function of the supercurrent --
allows us to probe the current-phase relation near equilibrium. Using a minimal
theoretical model, we can then link the sign reversal of the AC diode effect to
the so-called 0-$\pi$-like transition, a predicted, but still elusive feature
of multi-channel junctions. Our results demonstrate the potential of inductance
measurements as sensitive probes of the fundamental properties of
unconventional Josephson junctions.
