Well... It's not quite a dev kit, but I'm sure you get the idea.

After researching various combinations of processors, microcontrollers, and the necessary support IC's, I tentatively settled on using the ESP32-PICO-D4. It has integrated Bluetooth and WiFi (along with most of the required components for it) as well as some ram and flash and some other stuff. To be completely honest, I have only the vaguest idea of whether this will be an sufficient to implement all of the project goals.

Nonetheless, a while ago I ordered the ESP-WROOM-32 module, and it finally came in. As far as I'm aware, the module matches the pico-d4 version quite well in terms of specs, so it should suffice as a very cheap development platform.

Additional thanks go to Demetri Katsilometes for excellent photography.