qgis - Changing line type for boundary of two vectors?

I currently have two vector shapefiles containing polygons representing health geographies of England and Wales.

I would like to be able to change the line type for the boundary/lines between the orange and purple regions (Wales and England), in terms of thickness, colour, solid/striped/dot dash etc.

Answer

You can use a virtual layer to automatically derive the desired geometry.

Go to the menu layer / add layer / add/edit virtual layer and enter the query, replacing a and b by your region layer name

select  st_intersection(a.geometry,b.geometry) 
from a, b
where st_intersects(a.geometry,b.geometry)

Then style this layer with an adequate line symbol