I found a quite interesting video about creating a custom bluetooth remote for Sony cameras. The video can be found on youtube. It also links the used source code which can be found on github. Testing with my Sony a6400 I found out that the used pairing advertisement codes look different than explained in the video.
|Open for pairing||22ec00|
|Not open for pairing||22ac00|
The 8000FF00-FF00-FFFF-FFFF-FFFFFFFFFFFF commands used with FF01 in the video also work with my a6400.
|0x0107||transition to focus|
|0x0109||shutter fully pressed|
I also used the BlueSee software which is available via Apple App Store for free.
For getting it to work you first need to enable bluetooth and bluetooth remote. Further you need to pair the BlueSee software by going into pairing mode on the camera. The software will show pairing information which you just have to accept and from then on it worked.
With this it should be quite easy to build a custom remote based on a BLE capable chip like the suggested Adafruit nrf52840.