I think I have the solution !
I have found reasonably cheap current limit detectors on eBay : https://www.ebay.fr/itm/Current-Monitoring-Relay-0-05A-16A-24V-240V-Over-Under-Current-Protection-Relay/113187089821
It costs around 30$ and I finally received it :-) The build quality is better than the much cheaper noname DIN voltmeters I received as well. The provided documentation is actually useful :-)
I have chosen the 0.05-0.5A range version so I can trip from 10W to 100W.
A very good thing is the current sense input that is separated from the other circuits. The isolation makes it perfect to sense the output current that it will break.
However the break is momentary only. The duration can be from 100ms to 10s but I want a bistable system to ensure that the power is totally removed until I decide otherwise. A DPDT relay can be wired as a latch, its own coil being fed by the normally-open contact. A push-button in parallel would trigger the latch (only on demand), and the GRI8-01 is wired in series on the normally-closed contact, to disengage it when the current is exceeded. Yes, a basic set/reset latch.
I don't have a DIN-railed relay but I have powerful DPDT relays with 220Vac coils so I can try something!