In both of those cases there's a feedback loop setting the PWM dynamically. Even the error term of the PID or what have you would be super helpful.

There is no PID loop in the sense you mean. It's a hardware counter module that feeds a flip flop. There might be a free running ADC that is used to compare match against the counter module, or sometimes it's just a binary input like the AC signal zero crossing.

You don't need a CPU core to do this, and the older, cheaper parts do not necessarily have a CPU in them. There are even (iirc, very uncommon) designs with no digital logic save the switching.