I was able to figure out how to do the configuration UI. Pressing the "setup" button will display "SEtuP" on the display and create a WiFi network called "ESPClock". Connect to that and then surf to the web page at 192.168.4.1 and you'll get a form to put in the SSID, password, hostname NTP server and set things like 12/24 hour mode, enabling or disabling the 10th of a second digit and setting the mode for the colons.

I was also able to perform a rudimentary accuracy check on the clock. I took some slow-motion videos of the ESP clock prototype next to one of my GPS clocks. The iPhone slo-mo video seems to me to be running at about 120 FPS or so, so any given frame is maybe 8 ms or so away from its neighbor. Immediately after startup, the two clocks were changing the tenth-of-a-second digit about 6 frames apart, which is not great, but after sitting for an hour the two clocks were changing in perfect unison. Even at the start they were within 50 ms of each other, so that's still not too much to complain about. I'm certainly confident that it'll be just as accurate or more than the Pi clock I used to have.