I already had my code for the keyboard, but I had to modify it slightly, so that it would communicate over the TRRS cable with the other half, to receive the keypresses from it. Initially I assumed that the TRRS cable just connects the TX and RX pins, crossed — since there are 4 wires, two used for power. Only after some head scratching and probing the connections I noticed that something is wrong. I asked the author for a schematic, and turns out that only the RX pins are connected, and one wire is just left unused.
This turned out to be a bit of a problem, because the SAMD21 can't use the RX pin for sending data using the hardware UART, and CircuitPython doesn't have a software UART in the bitbangio module. Eventually I just ended up cutting the trace on the right hand side of the keyboard, and bodging it to TX.