So yeah, it's best to drop the Vcc connection. We will power the ESP using its own regulator.
All GBS boards ship with a nice 2 pin power lead that can be soldered onto the ESP board on one end, and plugged into the "5V IN" port on the GBS.
It's still portable this way: Simply unplug the power lead and you can take the ESP adapter off

That said, I also recommend using all available ground pins to mate the ESP board with the GBS.
There's 4x GND on a NodeMCU, for example (I hope the other boards with that physical pin arrangements also have those as GND).
I'd have to check again, but I think the GBS has only one ground pin on the PLCC, right? That's too bad really, it should've been more ><
Using this setup, the ESP8266 is mostly transparent to the GBS power design.
Any signal pins are either inputs or open drain outputs (the GBS board pulls them up to 3.3V), ground is shared via the power cable and several board points.
Vcc from neither board has a defined path to flow and potentially try to equalize each other (only some negligible parasitics).