I checked all of those things first - I bought the fully assembled kit, so it is wired up correctly. I then tried just connecting the module to a USBtoTTL programmer and viewed the output on a serial monitor. Unfortunately, it just seems to be stuck in a reset cycle - specifically it boots up and then a few seconds later the wdt_timer resets it. The red and blue LEDs flash every 7 seconds in time to this behaviour. This explains the lack of AP.
I then grabbed the github code, set it to debug and flashed a Wemos D1 mini and connected that to the serial monitor. It worked first time and the AP was visible. So I have an issue here.
I bought a ready made kit that should work and I can only conclude that it was not tested, as this is the most basic check for the WiFi module. I need to install this kit for a client, so I don’t want to have to deal with fixing the WiFi myself. How best to get a working WiFi module replacement?
And could you tell me what version of the firmware would be on the WiFi module? I assume it is one of these releases