I changed the oil now. Because there were some contradictory advice (one advice: wait 10min, another advice: wait for long to cool to a safe 'warm' temperature) I decided ultimately on 20 minutes. It seems this 20 minutes was more like waiting to cool to a safe 'warm' temperature.
It seems that after those 20 minutes, when the generator was cooling down in room temperature for that amount of time, the oil wasn't very hot. After pouring all of the oil in the engine (0.5 liter nameplate capacity but it seemed that I only drained about 0.45 liters so some oil probably remained in the engine surfaces because the 0.5 liters of replacement oil I measured seemed to be bit too much), into a 4 liter plastic oil catch container, I measured the temperature of the oil in the container with an infrared thermometer. The reading was 50 degrees Celsius. Presumably when the oil was still in the engine, it was hotter, but after it touched the room temperature oil catch container, it cooled down to an equilibrium.
Next time I reduce the wait time to 15 minutes, and then perhaps to 10 minutes if the oil temperature isn't very hot at 15 minute wait time. I suspect with hotter oil I might get more than 0.45 liters of it out, so the change would be more "complete".
After doing the oil change, I can say that this design of generator has absolutely no danger of burning your hands with hot oil. The oil drain plug and fill hole cover is the same part, and you remove it and tilt the generator to drain oil. The generator in my case was on the first step of a staircase and the oil catch container below it on the floor (below the oil catch container I placed an insulating piece of wood and a newspaper to catch any spilled oil). Because you can remove the plug without any oil dripping out, and oil starts dripping only after tilting the generator, this eliminates any danger of burning your hands with hot oil even if the oil is burning hot.
I used gloves, but I can't imagine ever accidentally touching hot oil in this design of generator, so next time I might do the oil change without gloves. With work gloves, there's always the danger that the gloves are dirty and could theoretically introduce dirt to the engine.
Since the plastic oil drain plug is above the oil, and doesn't really touch oil in use (except the integrated thin dipstick is under oil surface), feeling its temperature can't be used as a reliable indicator of oil temperature.
Edit: a second data point.
I changed my lawnmower oil (a different engine than the inverter generator). This time I waited for 10 minutes. After the oil change which required few minutes of waiting for the hot oil to be poured, my inframeter thermometer measured 60 degrees Celsius for the temperature of the oil. Obviously during those few minutes, the oil cooled, so when it was pouring out from the engine, it was hotter than 60 degrees Celsius. But by how much, I don't know.
About the possibility of burning my fingers, this seems a bit remote. Tipping the equipment isn't hard (but on a Briggs&Stratton it would be hard since Briggs&Stratton oil can be changed only from below or from above, not from the side as on these Chinese engines), and I obviously wear oven mittens when tipping the equipment and holding the oil collecting container.
At this 10 minute waiting temperature (probably somewhat above 60 degrees Celsius but by how much, I don't know, as the oil had cooled for few minutes), I managed to collect 381 grams of oil. I measured that 0.5 liters of new oil is 417 g, so this 381 grams is around 0.46 liters. The specified oil capacity is 0.5 liters, so I managed to collect about 92% of it.
So, I think 10 minutes is probably an optimal waiting time for small engines. The temperature is sufficiently far away from the 85 degrees Celsius at which the oil collecting container can be damaged, and yet still warm that it flows easily. Also, less time wasted for waiting for the oil change. Most of the 10 minutes can be spent by collecting the equipment and materials needed for the oil change.