As far as signifigant direct story elements go…as in, stuff in the plot that comes out of nowhere if you go straight from the OT to the ST without watching the PT…the Darth Sidious acknowledgement is probably the main one, along with the whole idea of the Sith being this long standing organization/religion, which is important to Palpatine’s revival and his plans for Rey. In the OT the Emperor was, as far as we knew, just this lone powerful dude who managed to convince Anakin to betray the Jedi and become his attack dog. The PT is what worked in the whole Sith plotline.