It's pretty simple actually, and a 3D engine isn't going to make this particular thing any easier since the perspective in games like Zelda is just an illusion; adjusting a real z coordinate would just make the player grow towards the screen (and slightly upwards at a 3/4 perspective).
The goal is to just have 2 y coordinates. 1 for the actual Y position, and 1 for the Y position + fake jump height. The latter is also used as a displacement from the object's shadow, aiding the illusion.
Here's a clip from my Illusion of Gaia practice engine:
The "hard part" is making a custom jump mechanic with events, but there are some examples around the forum, typically in R0j0hound's examples. vy, gravity, a loop for detecting the landing, and you're good.
As for stairs, that's all fake too. The player just moves diagonally when going up side-view stairs, and moves upwards as normal when going up front-view.