Yaris Hybrid Engine Stalling

Those symptoms do suggest fuel delivery problems. Before replacing the fuel pump, have you checked the simple things? A bad fuel pump relay or even a corroded connector at the pump can act like a failing pump. With the hybrid system, correct voltage is very important. What have you checked so far? That will help narrow things down.

I've looked at the wiring and connectors, but I haven't thoroughly tested the cable or plug connection. How should I test the electrical connections to rule that out?

Given it's intermittent and there are error codes, a loose or corroded connection is likely, especially since the car is older. A multimeter is what you need. Check for voltage at the fuel pump connector when starting, and check the ground connection for good continuity. A voltage drop test on the wiring can find hidden corrosion inside the wires. Because of the hybrid system, I'd suggest professional diagnostics. It can prevent electrical problems and find the exact cause. If it is a bad fuel pump or just a loose connector, the repair might be around 95€.

Thanks for the advice. After checking the connections, the shop found a bad connector and the fuel pump connector was loose. The repair was 95€ like you said.