There are two ways to split a polygon - with SQL/MM standard function and a non-standard, PostGIS specific function.
Using the standard way, we'll have to add two nodes to existing edges and split them.
This is done with the topology.ST_ModEdgeSplit function. It accepts three arguments: the topology name, the edge ID, and the point geometry, and returns the integer ID of the newly created node. A new node is added to the topology, and the edge with a given ID is split into two parts. One retains the original ID, and the second is given a new ID.
There is also a ST_NewEdgeSplit function, which deletes the original edge and creates two brand new edges instead. Use it if you are into immutable data structures.
We'll split ...
