Not really an issue for me.  I use Octoprint and could see vast improvement in this product.  I would like a product that works better and is tailored to the Prusa printers.  

... I suppose one could make a custom ESP32 board with that same header, but it's not an off the shelf part like those original ESP8226.

Why would you think you going to need all that horsepower, IMHO the ESP01 is only needed to communicate the gcode to the handler... (like an replacement for Octoprint through the USB port) all the needed horse power is on the BuddyBoard the ESP is only to transfer data from WiFi to an internal bus.

my 2 cents

Until you try and upload a 30-50MB or more gcode file though a serial uart which is what that 8 pin header on the ESP8266 boards supports. Unsure how they will implement this, upload the whole gcode file and write it out to an attached USB drive to then print off the USB drive, or implement it like a virtual serial port over TCP/IP and require a host PC running prusa slicer to stream the gcode in realtime over the network? This second method keeps a PC tied up while doing the print and if for any reason the wifi goes down during this print, then you have a failed print.

Understood, but it is not like we are communicating with a supercomputer through this header.  It is relatively small packets of information.  

Reportedly, it already has some of this functionality on the Mk3S.  

Just do an octoprint setup, it's probably going to take years if ever for Prusa Connect to have any kind of functionality that octoprint can already do. Considering the system requirements of octoprint, I have a feeling Prusa Connect won't be able to have anywhere near the feature set anyways because of the specs of the processor on the buddy board. Unsure how much that processor is currently utilized just to drive the printer. Perhaps this is the reason for the slow development of this, perhaps they have found that a usable web ui just isn't doable without impacting the printing functionality.

Probably the better option they could have done than that ESP header would have been to just put a Pi compatible header on the buddy board, then you could have just put your own Pi inside the electronics box running octoprint or a Prusa customized webui firmware image for the Pi. This way as well as newer/faster Pi's come out you can just simply swap out the Pi rather than having to respin the buddy board to support a newer processor.

Strange, I use a Win10 PC. Guess I will stick to Octoprint for now. I tried it just out of curiosity :D

Yes, there is more than a black screen, but only little more.

The black screen is a problem with apple devices. If you use a Mac ore an iPad you will mostly see only a black screen (sometimes after 15 min or so the prusa connect site may appear).

With an normal Win 10 PC it works, but at the moment prusa connect is not very usefull, you see a temperature graph and the print progress.