U3 has PNP inputs with a single supply, so any negative voltage can potential forward bias the Vbc input junction instead of Vbe. The BC junction is much lower capacitance and higher resistance than the BE junction and will catastrophically fail when forward biased with any significant load. Thus the LM358 has an ABSOLUTE MAXIMUM input voltage of -0.3V. In case of load dump or short transient, the LM358 must be protected at all costs from not going below this voltage, so that the input differential pair can properly function and not become unpredictable below ground.
Thus I would use a Schottky diode for protection and not a Silicon diode for a lower threshold of 0.2V at low current.
TVS are special diodes that offer low capacitance but have a higher threshold voltage and are designed to switch in an avalanche mode for super fast transition times and extremely low ESR which can handle very large power transients. TVS come in varying thresholds starting above 5V so it would offer no protection for this LM358 input.
All CMOS logic has this kind of Schottky diode input ESD protection with diodes to actually both rails, but for different reasons to prevent SCR CMOS latchup.