In almost all microwaves, the control circuitry or mechanical switches only ever switch 2-3 power circuits: motor+fan(+bulb sometimes separately) and the heating (transformer+diode+capacitor+magnetron) high voltage circuit. It can therefore only switch the heat between 0 and max, usually in a slow (15-30s period) PWM cycle (that hopefully does not coincide with the tray rotation period). The inputs can be manual only, or sometimes there is also a scale, moisture sensor and microphone, along with thermal fuses for safety.
I think the pizza setting is just generic medium one with short 50% cycles to allow the heat to spread. The popcorn setting can be much more interesting:
https://www.youtube.com/watch?v=Limpr1L8Pss
You are right, QR codes are very easy to decode if you have them raw, even the C64 should do it in a few seconds, maybe a minute for one of those 22 giant ones. The hard part is image processing when decoding a camera picture - and that can be done on the C64 too if it has enough time and some external memory (or disks for virtual memory). People have even emulated a 32-bit RISC processor on the poor thing, and made it boot Linux.