I found the culprit: Athom is using this IC for powering the board:
And then, the voltage from output goes to AMS1117 to be changed to 3.3V.
Unfortunately, the output of KP3210SG was below 3V so poor AMS1117 was stealing another 1V as dropout - finally on ESP it was just about 2V - way too low for the board to work.
I changed the capacitor (470u/10) and on the output I got 5V.
So, either they did not manage properly the IC KP3210SG, or any of the “around it” elements got old (i.e. the inductor or capacitors) or anything else - or maybe even the IC KP3210SG itself is … poor quality - the biggest problem is: OPENING AND CLOSING the plug - since - unlike Sonoff thingis - you need to almost destroy the plug to open it, once repaired it does not look nice anymore.
I was lucky today with a bit of hot gun (to open) and a bit of glue (to close) but again: it does not look nice anymore.
That is all - I repaired today 2 out of many - I will try to repair all.
Shame on Athom anyway.