Now I got it working, you have to flash it with the UART adapter, I found the pinout on this side
PINs on header (verified with multimeter, WROOM module pin number in parens):
1 GND square
2 TX (35)
3 RX (34)
4 3V3
5 GPIO0 (25) - must be held low on reset
6 RST (3)
To let the programmer automatically reset the board: Connect pad 1 (GND) to pad 5 (GPIO0).
flashed with ESPHome Webinstaller:
https://web.esphome.io/
When connecting to the PC, you need to connect GPIO0 to GND and then click on Prepare for first use. After that, you can disconnect it from GND again—basically as soon as you see that the firmware is being written.
Wi-Fi was a bit tricky; I had to connect several times because otherwise the error
An error occurred. Improv Wi-Fi Serial not detected
kept appearing.
After that, the device was discovered in Home Assistant and I was able to add it. It was also found in ESPHome, where I could add it as usual.
So, now it’s time to get down to the real work.