Broken phone, broken screen and a broken digitizer. It kept on registering random touches on the SIM PIN screen, unfortunately blocking it. My backup phone does not offer to enter the PUK PIN, so I had to find another way to unlock the SIM. Thankfully I have a Mobian compatible Pinephone where ModemManager could be installed.

$ sudo apt install modemmanager
$ sudo mmcli -i 0 --pin=<pin_number> --puk=<puk_number>

Tips courtesy of https://discourse.ubuntu.com/t/entering-sim-passwords/19909.