Repetier, thanks for the answer!
Ok, I think there are few more things I should have mentioned.
The printer is not exactly RAPMS. It's Overlord Pro printer with Atmega2560 custom PCB (it ships with marlin firmware). Extruder heater is 40W, and heated bed is 160W. 4 motors are 10W each max (which is really 20W in total in my setup). I'm not sure what fuses they have on their board though. Here is one the thing - I measure the power usage with a power meter like this:
https://www.aliexpress.com/item/German-Type-EU-Digital-Power-Meter-Volt-Voltage-Wattmeter-Power-Analyzer-Electronic-Power-Energy-Meter-Measuring/32806564122.html
It shows average power draw every second and while printing the machine is doing everything - moving motors, turning on/off the extruder and heated bed occasionally to keep the temperature on, etc. So the power draw value that the meter shows varies from 40W to 150W, which is why I mentioned 150W (which is below 200W power supply is rated for) - it's max average power draw I saw with the meter during regular printing when heated bed was On. So PID was only keeping the temperature, not actively raising it. So theoretically it could shut off while printing too, but haven't seen that happening yet (and which is why having this sort of "power budget" could be useful as it won't let it happen even in theory).
So far it only being happening in one very specific case - start of the job, M190 is finished and printer starts moving down to turn on the extruder. It turns it on and boom - shutdown. While it's moving I see that the power draw on the meter is decreasing, but gradually, because heated bed PID is still driving it somewhat, that's why there is a moment when they both may be on for long enough to trigger protection in the power supply. It used to be much worse because SKIP_M190_IF_WITHIN was 3 (default value generated by Repetier firmware web configurator) which exaggerated the issue.
As for capping the Drive MAX for the heat bed PID, I already tried that (before I learned about SKIP_M190_IF_WITHIN). It had to decreased 30-40% in order to get it work reliably this way (which is quite a lot, so I was even considering replacing the power supply).
And as for using PDM, I can give it a shot, but which value is it? Here is what I see in Configuration.h:
/**
Heat manager for heated bed:
0 = Bang Bang, fast update
1 = PID controlled
2 = Bang Bang, limited check every HEATED_BED_SET_INTERVAL. Use this with relay-driven beds to save life time
3 = dead time control
*/
#define HEATED_BED_HEAT_MANAGER 1
I was reading about dead time control and I think it was different. So is it Bang Bang, fast update? Anything else I should setup to make sure that On impulses are not very long? (cause that what will probably trigger the issue)