However, as schufti mentioned, the voltage divider does not work the other way around - stupid me . Because I read that all GPIO has over-voltage protection, I "took chances" and cut off both second resistors from TX and RX, respectively.
And it does work now. I'm using the espressif FLASH_DOWNLOAD_TOOLS_V3.3.4_Win and flash the bin that I created with Arduino IDE to 0x0. Why the Arduino IDE is not able to do that directly, I have no idea.
Although the ESP-01 can be flashed and run with the self-made board, the blue LED is still always on. A little dimmer but always on. Interestingly, I can switch it off with
Serial.end();
pinMode(PIN_TX,OUTPUT);
digitalWrite(PIN_TX, HIGH);
Don't forget pullups (typ. 10k) on gpio0, gpio2, rst and ENWell, I don't have any, yet. However, my 5 ESP-01 are running fine. I'll add these on the next breakout board.
Thx & best