Oh certainly could be a fun project. So, I kind of wish I didn’t know about the following, but… https://www.tindie.com/products/crimier/framework-input-cover-controller/
There is of course room for another! Perhaps a different take or different aim.
If you’re still interested I’d be happy to suggest some things.
The keyboard, whether you connect directly to the keyboard cable or connect to the cable that comes out of the input cover, which comes from the touchpad pcb, you’re dealing with the same signals. The touchpad PCB doesn’t actually do anything except pass though the keyboard lines unchanged. It just serves to merge a few different cables into one, so that users can remove the input cover by only disconnecting one cable instead of several.
It’s the raw keyboard matrix lines. So you’d need to attach it to a MCU that can serve as a keyboard controller. The raspberry pi Pico can do this. And the FWL16 actually uses the very same chip, the rp2040. Just without the raspberry pi Pico PCB board. Others have guides on how to make keyboards using the rp2040, like adafruit. You can use some existing open source keyboard controller firmware. For USB keyboards, the one people use is qmk. For bluetooth or other wireless keyboards zmk is the most mature & popular, though there are a couple others. For wireless you’d want a different chip tho. A lot things you can just copy from other keyboards that use the same chip. The biggest change is that you need to enter the FW13’s specific keyboard matrix into qmk’s config files. It can be found here, Reusing Keyboard after Replacement - #11 by nrp Adafruit or maybe sparkfun might have a guide on keyboard matrices. Oh, and the cable pinouts are on FW’s github, github.com/FrameworkComputer/Framework-Laptop-13/tree/main/Touchpad#pinout.