How to implement the mouse click highlight on StaticMeshActor of the scene when running?

You need two things:

One is evaluate the object under the cursor.
That is achieved with ‘Get Hit Results Under Cursor’

This example displays the name of the object under the pointer:

Second is create a special material that offsets the geometry.

The trick is duplicate the outlined static mesh and assign this outline material to it.

here is a simple blueprint example:

there is another technique using post processing volume but is a bit more complcated: