Well, Deponia on PS4 was actually made with a version of Godot, so it has to be possible.
I think for really complex 3D modeled levels, you can render a depth map from Blender and then use this as the base depth texture (well you can do this like in lower level APIs, not sure if Godot exposes this for you). That would be useful for a Resident Evil 1 type of game.
For a 2D point-and-click, that may be overkill (though I guess possible if you want to paint a depth map by hand). Another, and probably the most logical option, would be to save out individual object images with an alpha map and assign a z value to them. You could write code that would change the players z value as they moved through the world, and then swap the layer they are on to make them go behind a pole or a garbage can or whatever.
You can use the property z_index to adjust the drawing order.
https://docs.godotengine.org/en/stable/classes/class_node2d.html#class-node2d-property-z-index
You can give the static objects a fixed z_index, and then you just need to code the part that adjusts the player z based on where they are standing. How to do that will depend on how the camera angle are set up. One simple way is to map lower positions on the screen with a higher z index, and then ramp down to the top of the screen. You'll have to get a good range of values though, and I'm not sure this would work with lots of objects or complex camera angles.
You could also place a plane floor model (behind the real background) and do a raycast from the mouse to get the z value and use this for the z index. You'll need to match the floor to each background image, but this would give you a lot of control and you could match it up better. However, if you only have a few foreground objects, maybe this is a lot of work.
