Going in the other direction: recent Intel laptops with Thunderbolt should support USB gadget mode. In theory, this would allow a Linux laptop to emulate keyboard and mouse input to an iPad Mini portrait sidecar, with seamless kb/mouse context switching onto USB, as the cursor moved into the configured virtual viewport of the iPad "monitor".

Similar to synergy/barrier/input-leap, but using USB gadget mode instead of local network, since iOS wouldn't allow installation of non-Apple keyboard-mouse remoting software, https://github.com/input-leap/input-leap

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