After using Spatial Operations Difference, how do I add missing vertices to the areas?

Rubric124

I use the Spatial Operations Difference in scripting a lot, but my main focus is adding vertices to the area features where they got cut at. One area would have the vertex, but the other even though it meets at the edge does not. I would like to get this automated, but I do not know if the current add vertices at intersections truly works. Many thanks!