ESP8266 controlling RC car. Voltage drop, ESP shuts down when I increase motor speed
The ESP chips are notoriously sensitive to power supply voltage droop. You appear to have essentially zero decoupling, filtering, reservoir capacitance for the ESP8266.

Suggest using an isolation diode and a separate "reservoir" capacitor just for the ESP.  The diode will keep the dedicated ESP power reservoir capacitor from feeding back into the other parts of the circuit like the power-hungry motors, etc. I would use something in the thousands of uF (as big as the project will allow).   As your experiments showed, not clear what that 3.3V regulator is doing for you??