How to clean up a large plaster penetration
I'd just remove the plaster the rest of the way in the area of interest and replace it with backerboard / cementboard.
Tile is expensive in both materials cost and labor.
Putting tile on a dubious substrate is, therefore, a poor choice. If the substrate fails, your expense in both money &amp; time invested is lost. The slight additional money and labor to provide high quality substrate for tile is well worth it.
You could do any standard large-hole drywall patching technique if you would rather. I would not advise that, and I would not advise tiling the wall (beyond the hole) as it stands, based on these pictures. You might get away with it. You might not.