Welcome, Peter.
Sorry about your situation. Person or persons who installed that nominal half-inch plywood subfloor should be behind bars, but that's another issue.
The only way to make that subfloor usable for a ceramic tile installation is
if the surface is in near pristine condition, you glue-laminate another layer of nominal half-inch plywood over what you've got using a full spread of wood glue and lots of screws.
If, instead, you elect to install your 3/4" plywood over what you've got, I recommend you do so as though the original half-inch material were not there. Fasten the 3/4" to the joists and consider that you have a single-layer subfloor that's thicker than the original.
My opinion; worth price charged.