Ok, report: The China control module arrived & I had a play. It's the "TCB-NE PT100" which is specified at 12V/12A up to 24V/10A. The unit operates as a buck converter with switchable output polarity with +-1000 steps resolution. It can reduce maximum power going to the peltier, at the expense of control resolution by setting a lower maximum allowed duty. The duty is calculated by PID from temperature difference "Set Value"-"Read Value" at an interval between 100ms to 3s. To have stable regulation, the interval has to fit the speed of your thermal feedback. Each time a new duty value is calculated, it reports over serial. Also you can have manual interrogation instead. So far I did run it at 12V/4A max and it stayed totally cool so I have no reason to doubt the numbers. PCB seems well made, "Sam Young" capacitors. The unit has two error & ready logic outputs and a disable logic input. The Aliexpress seller send only the chinese manual, but shafan-oe.com seem to be the primary source and I got a prompt response in good english and the english manual from them. The official seller is shafan-store on taobao. PID values can be modified on the fly and will be used on next cycle, so with a bit of scripting on the pc side more complicated stuff (different P for heating and cooling as a first step?) can be wrapped around. All in all it is a simple unit without much bells and whistles, seems to be originally made for industrial temperature stabilisation of optical elements. Verdict: It does deliver for its price, at ~1/5 compared to more professional units I am happy with it.
Edit: Also, if you have hints on how to optimally set interval with regard to thermal feedback delay, I'm all ears