I got a chance to look up the data sheet today for the motor driver, and it was basically that.

From what I read the 5v output (the L298N uses a 78M05 regulator for 5V) will completely cut out due to the voltage sagging when the batteries are under load as the minimum voltage it can run on is 7volts. The 78M05 also has a max output limit of 500ma's. From what I could find the esp32 cam when using BT, and WiFi pulls about that much. The 78M05 was probably getting very hot if not close to burning out so it is probably a good thing it was shutting down like it was as if it didn't it would have probably burnt up the regulator eventually.

Also something minor that battery you plugged into the ESP 32 will probably cause issues when it discharges a little as the ESP32's min voltage is 4.4v. But if you keep it topped up it would probably last as long as the batteries in the vehicle.

BTW there is another reason I looked into this, and that is because I have 2 project ideas for ESP 32 cams that I have been thinking about implementing which could have ran into a similar situation you did