This is really interesting.  Does this mean it's possible to have the ESP32 both connected to one network, while broadcasting it's own network at the same time?   Would it be possible to use the ESP32 as a pass-through bridge for [device] -> ESP32 -> WiFi network, allowing the device to access both normal traffic on the WiFi network, as well as the ESP32's own internal page?  The reason I ask is that iPhones are notoriously difficult to connect external devices to, especially if they require high-bandwidth.  One of the things I've been exploring is connecting the iPhone to a device that poses as a wifi access point that allows normal wifi access, but also is able to serve it's own data to the device (either through an app, or just presenting a webpage through safari).  But it's not entirely clear to me that this is easily done with an ESP32 -- I've been investigating using a Pi Zero W with a second wifi dongle over USB, but it's a lot of extra space/power. 

Absolutely yes it is possible to have an ESP32 both connected to a network while broadcasting its own wifi. However, since there's only one radio both have to run on the same channel for this to work.

With the SDK, it's done automatically: broadcasted wifi will automatically tuned to connected wifi channel if they are different.

What you're asking to do would be some kind of low level routing. Pretty sure it's possible, but I don't know the inner working of it.

That's really interesting -- thanks for the information!   I'll have to read more into this -- I've mostly been tinkering with the Arduino implementation for ESP32, but it sounds like going under the hood might offer some impressive capabilities.