  We perform supercurrent and tunneling spectroscopy measurements on
gate-tunable InAs/Al Josephson junctions (JJs) in an in-plane magnetic field,
and report on phase shifts in the current-phase relation measured with respect
to an absolute phase reference. The impact of orbital effects is investigated
by studying multiple devices with different superconducting lead sizes. At low
fields, we observe gate-dependent phase shifts of up to ${\varphi_{0}=0.5\pi}$
which are consistent with a Zeeman field coupling to highly-transmissive
Andreev bound states via Rashba spin-orbit interaction. A distinct phase shift
emerges at larger fields, concomitant with a switching current minimum and the
closing and reopening of the superconducting gap. These signatures of an
induced phase transition, which might resemble a topological transition, scale
with the superconducting lead size, demonstrating the crucial role of orbital
effects. Our results elucidate the interplay of Zeeman, spin-orbit and orbital
effects in InAs/Al JJs, giving new understanding to phase transitions in hybrid
JJs and their applications in quantum computing and superconducting
electronics.
