I got this kit to practice soldering and try out QMK before building something a bit more interesting. I learnt many things in the process, most importantly that my soldering still needs more practice.
I used a ProMicro RP2040 MCU, and this kit requires the firmware to be compiled with the flag -e CONVERT_TO=rp2040_ce on the compile command in order to generate the required .uf2. This wasn't obvious to me at all, but the support person responded to me quickly with this info.
Even then, *spoiler alert* I couldn't get the onboard LED to light as written, and decided to modify keyboard.json to specify the RP2040 and avoid the need for conversion. With the new mappings, the matrix is "cols": ["GP23", "GP20", "GP22", "GP26"],
"rows": ["GP21"]
and the LED pin is GP17. This worked a treat :)
I still don't have a functioning 4th key, but I suspect that is entirely related to said poor soldering.
General things about assembling the kit: I didn't push my switches in far enough before soldering so I've got issues with spacing. I had to cut short the pins to get the back on (but I think I would have anyway). The connectors on the MCU I used are really tiny and don't run to the edges, unlike Arduino style boards, and they were really hard to solder. I think next time I would test the circuits with a multimeter before attaching the MCU.