Usually, every two to three thousand miles, when I switch the engine off, there is a loud once only beep, and the oil can icon comes on as you have shown. So then I know I have to add a litre of oil as soon as I can, but definitely before doing another 250 miles (I read somewhere) which is more than most peoples daily commute I think is the reasoning.
Anyway, if I drop the 1 litre in before going to work the next day, I don't bother checking the level until I'm just about arriving back home in the evening, by which time the car has done 25 miles.
I press the RHS button (I think!) between the dials and I see a graphic of four or five blocks building, resetting, building, resttting, building.....until it hopefully stops on all the blocks showing and the lettering "OK!" as well.
So I'm assuming none of this block building buisiness is working on your display.
But the oil icon coming on seems to show that the oil sensor is working.
Does the other button (S/R on the left) work? This resets the trip counter and I think you use it to reset the clock on the dash when the clocks go back.
Another job which I will probably get round to doing in a month or two
Just wondering if it could be a fault related to the small orange lettered display, or the buttons connecting to it.