Sorry for the rather noob question, can someone give a short explanation of how the GATT_CLIENT example in esp-idf is intended to be used?

The GATT_SERVER is straightforward, I can run it, connect to it from a phone, read/write to the two services which are advertised. But I'm not sure if/how the ...

This is great news. I already have HomeKit somewhat working on ESP8266, but it's using a RaspBerry Pi bridge for emulating the HomeKit API and doing the heavy lifting of encryption. I would love to beta test if something better is already in the works.