Hi Anna,
Thanks for getting back with your interesting solution. That's a handy 5V to 3V3 interface board for the ESP-01, and I'm adding that to my list of useful gadgets :)
Regarding the booting problem when using one PC USB port to power both the ESP-01 and the SC131; that can easily cause, as you suspect, the voltage supervisor triggering. The max current output of "traditional" PC USB ports is 500mA. ESP8266 devices are known to draw extra current when transmitting. The USB port is probably limiting the excessive current. A small 5V power supply, like the 2.5A ones used to power a Raspberry Pi, would be ideal to power both the SC131 and the ESP01.
Note that a poor quality USB cable can have a noticeable voltage drop and cause similar problems. That can be easily tested by using another, preferably shorter USB cable to see if it makes a difference.
Regarding my original post, the convoluted dongle "solution", which I mainly focused on was probably overkill. Not really a simple circuit to breadboard like you asked for.
That got me thinking, so I decided to design a simple adapter to be put on a bit of prototype board, that will work the same way as my dongle but more easily wired up. Something to note with the circuit is that it automatically lowers the retro serial port 5V Tx output to roughly 3V. That's done by the 10K and 15K voltage divider feeding the transistor base, so no extra voltage conversion is needed. In the other direction, the ESP8266 Tx output voltage is high enough for the retro serial Rx port input. Putting a 3K3 or so resistor in series is good protection to limit any potential excessive current.
I'm including the layout of the adapter prototype here in case anyone else reading this topic is interested. The layout can easily be transferred to a breadboard for testing. If making the board, put the components on top and connect them with some wire on the bottom.
Regards,
Paul