Of course the mirror is flat, 2-dimensional.
But the image in the mirror has all the characteristics of the 3-d volume on your side. If you change your point-of-view and look into a mirror the image contents change their relative appearance as if they were in the next room volume.
There is different information available from that different angle.
A photograph does not have different information available from a different angle.
You will get parallax differences at different angles but there will be the same information.
A hologram does have different information available from a different angle, hence it’s similarity to the mirror in that respect.