UPDATE: Based on further discussion, my new theory is described in this follow-up post with a new animation. The description of wall panels in this post is superseded by the new post. Check it out!
Here is a video provided by Disney Previewing the attraction
The theory is, as the effect starts, the A and B panels move outward, and slide behind the stationary walls surrounding the area just like a pocket door. The edge where the door slides behind is obscured by the vertical timber elements in the room. Simultaneously, the C panel slides down eventually be flush with the floor. This design allows the mirror's edges to grow in three directions while leaving the space revealed 'open' to see the projection surface behind.
The mirror expansion could be done several ways.. but here is my speculation... The top part of the mirror is fixed stationary on the front surface of the the wall above the mirror. The mirror top edge expands horizontally by allowing the yellow and green segments to telescope out. In the start position, they are hidden 'inside' the blue portion.
The bottom part of the mirror is similar, the central blue section fixed stationary on the front surface of the C panel. The blue section moves down, allowing the cyan and gold segments to telescope out. In the start position, they are hidden 'inside' the blue portion. The blue side sections of the mirror could have been attached to the A and B panels like the others, allowing the corner pieces to telescope and 'float'. But this is not done because you can see in the videos, that the blue sections on the side actually move down as well as having telescoping action. I will speculate the mirror sides (or possibly all of them) are motorized to control the telescoping and are float over the side panels. Being attached at the top or bottom segment of the mirror. Powered telescoping may reduce binding if the speeds are off slightly in the wall panels.
The sum of these movements are illustrated in this crude gif
Now what about the projections?
The green magic effects are clearly projected onto the mirror frame from the area where guests are. Not looking around the room, I don't know if this is hidden in the ceiling using a short-throw lens or what.
But what about the mirror surface itself?
I believe this to be a surface behind the 'pocket door' panels that splits in the middle and splits left and right. I thought it may be doors that swing open, similar to the animation being projected, but the way the video terminates on the edge and doesn't skew.. it seems like the projection surface simply moves out of frame, rather than out and back.. like a door. I still can not make out any seem in the projection surface from the videos shared.. so I'm not real sure. But where is the projector? Possibly in the ceiling in the second room so you don't see the bulb's light looking into the door? Can't tell...
So what do you think? How do you think it works?