I also started something like this my self. But only to share my investigations for someone else interested as a kick-start.

I think that TCA8418 is more suitable for mobile devices. Full Qwerty with all the buttons needed (or fit) can be made from less than 60 buttons. TCA8418 has maximum of 80. It also releases phone's CPU from it's pain. Simplicity is cheap and beautiful. There is some drivers for linux but I leave this challenge for more experienced after I have one working model.

Right now I investigate what else components are involved. I've made circuit model using ExpressSCH. Keyboard has full layout of keys wired to columns and rows so that each key has it's own row-column -combination. Pullup resistors.

What else I need to complete this circuit?
Can TCA8418 be wired directly to the SCL, SDA, INT, GND?
If it can, what I do with RESET, Vcc?
I don't know what is inside Jolla but I think there isn't much since it's made to receive.

Also started on some CAD models with Inventor.

Everything you share dirkvl will somehow speed up the process. I won't stop until we have a product! What do you think about 8418?