Hi, my post may not be helpful to the original poster, but I have been searching for the same thing for the SpeedyBee F405 V4, and it led me here and nowhere else. So, this might help someone.
I have been successful in re-flashing the ESP32-C3 on the SpeedyBee board with DroneBridgeESP32 firmware. I soldered UART Tx, Rx, and GPIO9 to GND and powered it up. Unfortunately, I did not save the first boot log, but unlike the original poster, mine showed another boot method and was ready for upload via serial. So, I closed the serial terminal and ran esptool. It went smoothly, and now I am running DroneBridgeESP32 on the SpeedyBee board. I had to reverse engineer the connection of UART between the ESP32 and STM32F405. It is connected as follows:
STM32 PA0 (pin 14) —> ESP32 GPIO5 (pin 10)
STM32 PA1 (pin 15) <— ESP32 GPIO3 (pin 8)
In DroneBridge, set the Tx pin to 3 and the Rx pin to 5.
It works with Ardupilot perfectly at 921000 baud.
There is one drawback: you will lose the functionality of the four LEDs signaling battery state.