Fortuner Overheating and Coolant Spill

Sounds like a potential CAN bus issue or a faulty sensor sending incorrect data to the ECU. Have you scanned for any diagnostic trouble codes (DTCs)? A connectivity issue might trigger those symptoms.

I scanned it and got a code related to a generic control module communication error. Could a defective cable or plug connection really cause all these problems, like the overheating and coolant spill?

Yes, a defective cable or plug connection on a critical sensor can absolutely wreak havoc, leading to misreporting and cascading failures. Best to get the wiring and connectors checked out thoroughly, or head to a workshop.

I took it to the shop, and it turned out to be a corroded connector on one of the sensors, just like you suspected. New connector and cleaning fixed it, total cost 95€.