I have done doors similar to what you are considering. I did one door which was 80" high x 24" and we made it 1 3/8" thick just as we would make an interior door. We put a 1/2" plywood panel into the dado and we used a mortise and tenor construction and then glued on the mirror.
If you do glue on the mirror, be sure you spray on a protective coating before you apply the glue and use glue designed for that purpose or the mirror will develop cracks.
Hinging might be an issue. So you will need to think this one through. For the door above, we were making a mirrored door in a closet which was designed to hide a cabinet which hide a safe. For this door, I use three Soss hinges. If you do not have a CNC, something like this is really difficult.
I also did some tall cabinet doors, not this tall or this wide, where we used 3/4" stiles and rails. There, I put 3/16" mirror into a frame that had a dado so that it could be dropped in like you are proposing. We used silicone to secure the mirror. Then we mounted 1/8" plywood onto the back of the door. We screwed the plywood on to the frame and finished the plywood. We put cardboard in between the glass and the 1/8" plywood. The plywood was larger than the mirror opening. We had to make cutouts for the hinges. For these doors which were about 18" x 60", we used four cabinets hinges per door.
I hope this helps.
Paul