take a photo from the front edge... what kind of raw edge is on the sides?

the top step can be recessed, but how rough is the side pieces?

Overlap stair noses are common in vinyl flooring. Nothing to do with your contractor. That's the most common way of handling stairs by manufacturers. I don't like it either. Next time, do wood. Or, do it now.

I have no clue what kind of flooring but I have never seen that done with LVP and now most companies make perfect stair nosing for LVP. Contact Hewn they make nosing for their LVP

That looks insane. It's a big tripping hazard -- and at the top of a stairway! How could you have lived with that for 2 years? If it's a vinyl floor, find a competent floor man/woman who can do something like cut into the flooring and insert that nose piece so that it's level with the result of the floor. If it's wood, find a floor man/woman who lays wood floors and can cut the underlying wood and set the nose piece flush.

Is this how it is existing now? Cut the lower flooring out to place the top pieces at the same level. Is your contractor now done or was this all 2 years ago?

Is this the trim piece he installed?

This is from Hewn's website and is the only stair trim piece they show.

That looks pretty good to me and nothing like what you have , this is from Hewn site and the profile katinparadise posted

No picture of floor and top step where the trip hazard is located?