Drains like that (speaking from first hand experience) are disasters waiting to happen. All it takes is for a big leaf or two to lay down over the grates to block the flow of water. Then the stairwell fills up until it flows over the threshold into the basement.
Here's what did. I found a short piece of PVC pipe that would fit down into the existing pipe. ...
Concrete floor paint, as used in showrooms and garages will do just fine. Different colours are available, and some mix with epoxy, giving an even harder finish.
Might be an idea to mark the edges of the treads in a lighter colour, for safety reasons.