2.5D with 2D backgrounds

You could do that. It would take some planning and quite a bit of work to map the characters like that. I couldn't tell in a couple videos I saw of Syberia that this is how they created the environments, so I presume that you know that from somewhere else.

One Idea I can think of is to create a room or any space out of colliders that matches up with the 2D background exactly from the view of the camera. So a floor (any flat collider) collider would line up with the part of the image that represents the floor. Then you can have the player move around in the 3D space, or 2.5D and it will look like he is moving on the image.

If it is 2.5D like a side scroller, then all you have to do is create colliders that line up with the floor again, and you could add colliders for obstacles.

I just found this is what I'm also planning to do, but how do you implement parallax based on several layers of 2D images? Like for example a chair or a table is in a plane nearer to the camera than the 3D character.