WiFi power issues

Ahh, I just googled and took the top hit, which was wrong :) Still, https://forum.makehackvoid.com/t/esp8266­-operating-voltage-range-and-sleep-curre­nt/286 implies that they tested and 2.3v seems to work ok. Perhaps not under load, but there's a lot of leeway.

On the Wifi that VUSB pin is connected straight to USB 5v - so it should be fine - however I guess it depends how it's connected.

I will note, that quite often I experience an issue where I can't flash to the Espruino once something has gone wrong with the WiFi. I wonder if this is a symptom of the STM32 browning out?

It could well be, yes... Since the ESP8266 driver's all JS at the moment you should be able to Ctrl-C out of pretty much any execution regardless of what's happened.

Do you have something like an oscilloscope that you could connect to the 5v and 3.3v lines? It might help to narrow this down quite a lot.