How can I fix my concrete front porch landing
If the existing landing and porch were poured together, there's probably rebar embedded in both. Breaking off the old landing without disturbing the porch below may be difficult. Plus you will need to add rebar to whatever new step you add and it would be best if it were embedded in the porch.

I doubt you'll have much luck just adding onto the depth and then skimming over the entire thing. Concrete shrinks a little as it dries and I just don't see this staying together for very long, and as soon as water gets in that crack then it's all over.

You may find it easier to highlight the step transition to make it more visible instead of tearing up your entire porch just to add 6" to the landing. E.g. maybe a door mat, some potted plants, or even installing a railing would help draw the eye to the transition.