I'm using blender 2.92 and trying to apply "merge by distance" on a mesh. You can see in the gif that I first select the vertex to show it is overlapped, then "merge by distance". I expect that after the "merge by distance" was applied I would end up with only one vertex but we can see that nothing changes after I apply it.
For context, I created the mess by starting with a cube, scaling on the X axis then I scaled the two sides to 0 on the x axis to create an edge shape so at that point there are two edges overlapped. I'm guessing it has something to do with how I attempted to create the edge on this mesh?