Hybrid superconductor(S)-semiconductor(Sm) devices bring a range of functionalities into superconducting circuits by introducing Josephson field-effect transistors (JoFETs): Josephson junctions with a gate-tunable critical current. In particular, hybrid parity-protected qubits and Josephson diodes were recently proposed and experimentally demonstrated. Such devices leverage the multiharmonicity of the Josephson current-phase relation (CPR) in highly transparent S-Sm-S junctions, a so-far underutilized property. In this work we report an experimental study of superconducting quantum-interference devices (SQUIDs) embedding JoFETs fabricated from a SiGe/Ge/SiGe heterostructure grown at CEA-Grenoble. The single junction CPRs shows multiple harmonics with gate tunable amplitudes. In the presence of microwave irradiation, the appearance of integer and half integer Shapiro steps confirms this observation. A combination of magnetic-flux and gate-voltage control enables tuning the SQUID functionality from a nonreciprocal Josephson-diode regime with 27 % asymmetry to a π-periodic Josephson regime. Within a double SQUID device, we are able to quantitatively characterize a regime where the sin(2φ) component accounts for more than 95 % of the total supercurrent. Finally, this result is placed into perspective through a discussion of the implementation of a cos(2φ) parity-protected qubit within the Al-Ge/SiGe hybrid platform.