There is a currently a limitation with polygroups with a hole like that. You can use the polygroup cut tool to split the group into two sections and then you can use insert edge to clean up the polygroups topology.
Also keep in mind that a polygroup is a group of triangles, not a polygon. The polygroup can have any number of boundary edges. You can use simplify or retriangulate on the resulting polygroup as well if the triangle topology is not optimized.
That’s good to know, would be nice to have an option when cutting though (to cut the faces), because the average user will see that the tools stop working when such geometry exists and will think there is a bug with them. A warning message, or a prompt when cutting, to help ease into what is happening. This is why I reported this as an issue, because there is no tell that what you posted is the next step and half of the tools that rely on edges stop working without telling you why.