Does over-mount fire-clay apron sink need additional framing to support
YES ERR on the side of caution and add support to your cabinets.
The sink you have linked to shows the counter running under the edge of the sink. This not structural support, the structural support is provided by the cabinet side that should be directly below that edge. You should not have a counter that is floating or cantilevered out over the edge of the cabinet as this would not provide enough support for the sink, you would need to add structural support under that edge to insure proper support.
Is your cabinet the appropriate size for this sink ?
It is critical that the support, cabinet or cabinet with added ledger board, be sized correctly. I.E. the space from side to side must be exactly what the manufacturer states in the specs for installation.
The PFD installation instructions for your sink say -
" 4. Sinkology farmhouse sinks are considered fully support when ¾”
inch or more of the rim is supported on three sides".
If your cabinet does not have ¾” inch side panels you can had some material to get it to the correct thickness, Use construction adhesive and screws to attach.
Once the sink opening is the correct size the counter is then cut to size, or manufactured, and installed then the sink can be installed.
Concerning the back support for the sink, ledger board, the PFD on your sink does not tell me about the back of the sink. You need to make sure the ledger board on the back of the cabinet is at the correct height for the sink to sit on. I would assume that that will be the the same height as the counter that the sides of the sink are sitting on but that may not be the case. If that is the case then the back wall of the cabinet is not going to be that height so you ad a ledger board that will sit up above the top edge of the back panel to the correct height, A 1x4 should be good as only an inch or less will be above the top of the panel leaving plenty of board to glue and screw to the panel.
Since this is against the wall, if you could screw into the studs that would be best but you need to know where the studs are and where the plumbing and electrical are so you do not screw into them.