I had Eric give your video test a shot and he was still not able to get the 23 verts.
He made three cubes in his initial test:
1 - No Smoothed edges
2 - single smoothed edge
3 - all edges smoothed
the results were that there were 24 verts for all three.
Here is the file: https://www.dropbox.com/s/crlajm1te1ac1qj/Cube_Maya_Test.fbx?dl=0
In the next test he made a cube with a single smoothed vertex. This resulted in three faces smoothing and vertex count of 22.
Here is the file: https://www.dropbox.com/s/sphr03og9sqm57n/Cube_Maya_Test_2.fbx?dl=0
Now to take a moment and go back to the original issue with regards to UVs and lightmaps.
I didn’t see a difference between your UVs and I’m not getting a difference on these that I can see either. With regards to how smoothing works. The vertex normal is what is changing here. you can take a look at the second asset above and see how the vertex normals are aligned for the smoothed edge vs the hard edge.
You shouldn’t have an issue with your mesh here I believe.
Tim