I'm doing it with Bluetooth.

Gave up fairly quickly on using linux bt stack as it's... Not fun.

Instead I have a ESP32 dongle style board [0] connected with usb to my computer, it present itself as BT HID device to the iPad and communicate with the computer via serial.

Still wip, but overall it works for my main use case(skipping songs & managing volume).

[0] https://www.waveshare.com/esp32-s3-lcd-1.47.htm